Machine Learning Models of the Geospatial Distribution of Groundwater Quality: A Systematic Review

Abstract

Assessing the quality of groundwater, a primary source of water in many sectors, is of paramount importance. To this end, modeling the geospatial distribution of chemical contaminants in groundwater can be of great utility. Machine learning (ML) models are being increasingly used to overcome the shortcomings of conventional predictive techniques. We report here a systematic review of the nature and utility of various supervised and unsupervised ML models during the past two decades of machine learning groundwater hazard mapping (MLGHM). We identified and reviewed 284 relevant MLGHM journal articles that met our inclusion criteria. Firstly, trend analysis showed (i) an exponential increase in the number of MLGHM studies published between 2004 and 2025, with geographical distribution outlining Iran, India, the US, and China as the countries with the most extensively studied areas; (ii) nitrate as the most studied target, and groundwater chemicals as the most frequently considered category of predictive variables; (iii) that tree-based ML was the most popular model for feature selection; (iv) that supervised ML was far more favored than unsupervised ML (94% vs. 6% of models) with tree-based category—mostly random forest (RF)—as the most popular supervised ML. Secondly, compiling accuracy-based comparisons of ML models from the explored literature revealed that RF, deep learning, and ensembles (mostly meta-model ensembles and boosting ensembles) were frequently reported as the most accurate models. Thirdly, a critical evaluation of MLGHM models in terms of predictive accuracy, along with several other factors such as models’ computational efficiency and predictive power—which have often been overlooked in earlier review studies—resulted in considering the relative merits of commonly used MLGHM models. Accordingly, a flowchart was designed by integrating several MLGHM key criteria (i.e., accuracy, transparency, training speed, number of hyperparameters, intended scale of modeling, and required user’s expertise) to assist in informed model selection, recognising that the weighting of criteria for model selection may vary from problem to problem. Lastly, potential challenges that may arise during different stages of MLGHM efforts are discussed along with ideas for optimizing MLGHM models.

1. Introduction

1.1. Groundwater and Contamination Hazard

Groundwater is a crucial source of water for different sectors all over the globe, including both developed and developing countries. Agricultural, domestic, and industrial uses account for 69%, 22%, and 9%, respectively, of groundwater abstractions [1,2]. With the increasing populations and correspondingly increased industrial and agricultural economic activities, there are global concerns about both the quantity [3,4,5,6] and quality [7,8] of these resources. Focusing on the quality, groundwater contamination has emerged as a serious problem arising from both anthropogenic and geogenic (natural) processes [9]. Arsenic [10], nitrate [11], fluoride [12], and iron [13] are among well-known groundwater contaminants threatening millions of lives or well-being or otherwise impacting drinking water quality, especially in Asia [14,15]. Concerns over groundwater quality are reflected in the Sustainable Development Goals (SDGs), notably SDG 6, which includes specific targets with respect to serious inorganic contaminants, notably arsenic [16].

Groundwater quality (GWQ) mapping is a fundamental step toward sustainable management of groundwater resources by identifying spatial variations in contamination levels across the study area [17,18]. A GWQ map—as a general term—can be obtained by modeling the probabilistic distribution of groundwater contaminants with respect to environmental and geochemical conditions, and calibrated by alignment with actual (measured) concentrations of contaminants.

Whilst different terminologies, such as groundwater hazard mapping (GHM), groundwater vulnerability mapping (GVM), and groundwater risk mapping (GRM), have been used to address the process that results in a GWQ map, it is acknowledged that these key terms differ in meaningful ways, owing to their underlying conceptual distinctions. Hazard is viewed as a threat, a pre-existing condition that can turn into a risk depending on the effect of endogenous and exogenous factors, whereas vulnerability is perceived as the interactive effects of the social and physical aspects of a system regarding susceptibility to the hazard increasing in the future, and risk is calculated as a function of hazard, exposure, and receptor-vulnerability [19]. Notwithstanding the widespread use of GVM in the literature [20] and acknowledging its relevance (see Text S1), GVM mostly relies on aquifer properties alone to predict future hazard; hence, this study adopts the term GHM in light of the probabilistic essence of the modeling based on the actual current presence of contamination. Henceforth, GHM is used to refer here more broadly to studies that have conducted groundwater hazard/vulnerability/risk/susceptibility mapping.

1.2. Geospatial Analysis and Models

Geospatial analysis—described as a combination of analytical models and spatial software applied to geographic data—is a useful approach for understanding spatial patterns (i.e., distributions) and discovering relationships between various parameters [21]. In all GHM efforts, the use of geospatial analysis is essential [22,23] to account for spatial variations of groundwater contaminants [15,24]. With the help of remote sensing and tools such as geographic information systems (GISs), it is viable to readily acquire, analyze, and visualize environmental and geochemical data for GHM. Exploring the spatial relationship between groundwater hazard and influencing factors enables experts to create better hazard maps and identify critical areas for remedial action or mitigation. Various methods including statistical techniques (e.g., Dempster–Shafer [25], frequency ratio [26], weights of evidence [27]), decision-making techniques (e.g., technique for order of preference by similarity (TOPSIS) [28] and analytic hierarchy process (AHP) [29]), and artificial intelligence (AI) tools [30] have been suggested for this purpose. This study focuses on machine learning (ML), as a branch of AI tools that has been widely used in the geospatial analysis of GHM. This context is hereafter referred to as MLGHM.

1.3. Machine Learning

ML models have attracted tremendous attention for analysing and predicting high-dimensional parameters, in part due to advantages such as handling non-linear and automatic computation compared to conventional statistical techniques. These models are capable of learning the dependencies between inputs and output(s) parameters to perform regression and classification tasks [31]. In the first phase, the models explore ‘training data’ to learn the pattern, and, in the next phase, the quality of their knowledge is tested using the second set of data called ‘testing data’.

A general classification of ML models is shown in Figure 1 [32]. There are three major categories of ML models, viz. supervised learning, unsupervised learning, and reinforcement learning. The first two categories are employed for the common prediction and classification tasks. In supervised learning, the inputs are paired with known targets (i.e., values/classification labels), and in contrast, unsupervised learning represents a training wherein the inputs are not associated with particular targets [33]. In Figure 1, another category is shown called semi-supervised, which is defined as a learning type in which some of the data is labeled and the rest is unlabeled [31]. Further explanations regarding the subsets of these groups are provided in the rest of the article.

1.4. Scope and Objectives

Considering the importance and popularity of ML models for groundwater quality modeling, it is important to update the current knowledge about the latest developments in this field [34]. While there are many published reviews of the application of ML models in general and more particularly to surface water quality modeling [35,36,37], fewer studies have been specifically dedicated to groundwater (see Table S1). Whilst these reviews provide useful insights to MLGHM researchers, there are a number of gaps in coverage, which indicates the potential value of a further and differently focused review. In detail,

(i)

Most previous evaluations of models have been largely focused on model accuracy without substantive further consideration of other model evaluation criteria, notably predictability, complexity and relevant penalization, and computational efficiency [38,39,40,41].

(ii)

Some recent reviews considered only a small number of studies [38,40,42], or were restricted to just a specific contaminant (e.g., nitrate [43]) or a specific ML (e.g., artificial neural network (ANN) [44]).

(iii)

There is some inconsistency in the use of technical terms in relation to ML [38,41],

Based on these identified gaps and limitations, the key aims of this study were as follows:

• Provide a systematic and comprehensive review of published MLGHM articles meeting stated inclusion criteria.
• Provide a descriptive analysis of MLGHM articles with respect to geographic distribution, target and predictive variables, and ML approaches.
• Consider the criteria to be sensibly considered in selecting the best ML model for a particular purpose.
• Ultimately, provide optimization-oriented suggestions to improve the effectiveness/efficiency of MLGHM.

Note that the List of Abbreviations can be found in Supplementary Information.

2. Materials and Methods

2.1. Survey and Criteria

The publication databases Google Scholar, Web of Science, and Scopus were searched for relevant publications written in English over the period of 2000–2024 using a combination of environmental, ML, and geospatial-related keywords as outlined in Table S2. These searches were supplemented by relevant publications from other sources (e.g., ScienceDirect, SpringerLink, Copernicus Publications, Nature Portfolio, Science, and Wiley Online Library), as well as a number of previous review articles.

Regarding the inclusion/exclusion criteria, as illustrated in Figure 2:

(i)

Only original research articles that were published in Scopus-Indexed journals (December 2024 list [45]) were considered.

(ii)

With some notable exceptions, only those articles in which ML analysis led to generalizing the prediction to unsampled subareas (i.e., GHM) were included. A few articles that did not satisfy this criterion were retained as they included a clear representation of the contaminant distribution in addition to presenting useful comparisons among controversial ML models (e.g., Ref. [46]). Hence, studies that were bound to merely numerical groundwater quality analysis were not included.

(iii)

Articles in which there were evidence inconsistencies in stated target or predictor variables were excluded (Refs. [47,48]).

(iv)

Articles in which it was not immediately clear whether the used models were ML-based (e.g., Ref. [49]) were excluded, as were articles that, notwithstanding that their models were categorized as unsupervised techniques, nevertheless described techniques that are widely considered not to be unsupervised ML. Such techniques included entropy model averaging (EMA) in Ref. [50], fuzzy-catastrophe framework (FCF) in Ref. [51], fuzzy membership framework (FMF) in Ref. [30], as well as the GA and Wilcoxon test in Ref. [52]. Note that the use of metaheuristic techniques such as the genetic algorithm (GA) for optimizing predefined frameworks (e.g., DRASTIC) is considered a popular, yet non-ML, approach for GHM. Examples of these studies will be discussed later.

2.2. Meta-Data

A total of 284 articles were found that satisfied the inclusion criteria. The following information was collected from each paper: country of study area, year of publication, ML model(s) utilized, modeled target parameter(s), predictive variables, feature selection techniques (if used), and optimization techniques/algorithms (if used). Further considerations regarding the study area of some articles can be found in Text S2.

3. Trend Analysis

An objective of this study was to describe temporal trends and the geographic distribution of MLGHM articles, and the considered target and predictive variables. The results and relevant discussions are presented in Supplementary Material (Section S1). The key takeaways were as follows:

(i)

There has been a consistent rise in the rate of MLGHM publications over the period of 2005–2024.

(ii)

Iran, India, and the United States are the countries with the highest number of MLGHM case studies.

(iii)

${\mathrm{N}\mathrm{O}}_3^{-}$ was the most studied target variable.

(iv)

Chemical characteristics of water and, to a lesser extent, textural and chemical characteristics of overlying soils were the most commonly used predictive variables.

(v)

Tree-based models (mostly RF) were the most favored feature selection technique.

4. Machine Learning—Review of Model Types

A classification of the reviewed MLGHM models is provided here, together with a summary of the frequency of use of each category/single model. A total of 676 (not unique) ML models were used in the surveyed articles, out of which 638 were supervised and 38 were unsupervised. The only application of semi-supervised models appeared in Ref. [53] for identifying the groundwater contaminant source. However, it was excluded from this survey due to not meeting the inclusion criteria.

Classification of ML models into further sub-groups was carried out based on pivotal sources, e.g., Refs. [31,32] and earlier similar studies, supported by expert knowledge. The results are shown in Figure 3, with classification details in Table S7 and relevant articles cited in

Table A1. Surveyed studies for the identified ML categories.

Type	Category	Reference
Supervised	ANN	[46,50,61,62,92,105,109,116,144,145,146,151,160,165,168,169,170,171,173,174,175,176,177,179,188,189,191,192,194,201,204,206,212,213,217,233,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315]
	NF	[69,105,124,145,147,174,175,177,180,181,188,189,190,191,315,316,317,318,319,320]
	Tree-based	[7,8,46,74,75,92,109,115,116,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,170,171,172,173,175,176,178,179,187,192,195,198,183,184,185,193,194,199,200,206,208,209,231,234,241,280,281,282,283,284,286,294,297,298,303,304,306,308,311,313,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383]
	SVM	[50,51,52,81,109,115,116,124,144,146,147,148,150,153,154,160,165,173,174,175,176,179,182,188,190,192,196,197,198,199,200,201,202,203,204,212,233,276,284,280,281,282,286,290,292,296,298,304,306,308,309,322,331,336,343,358,383,384,385,386,387,388,389]
	Regression	[74,75,86,116,144,145,150,152,155,157,163,169,173,176,179,182,186,187,193,194,195,202,203,213,241,285,296,303,306,308,309,311,318,319,320,332,339,341,343,347,352,356,357,366,376,377,383,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409]
	Probabilistic	[92,116,144,148,149,159,166,170,172,173,179,192,197,199,202,203,204,205,206,207,209,213,292,309,331,385,386,410]
	Ensemble 1	[46,92,114,116,144,146,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,169,178,179,187,192,193,195,197,202,209,241,291,298,306,308,323,332,336,340,346,347,348,350,352,354,355,360,363,368,372,377,383,385,386,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426]
	Ensemble 2	[105,109,116,124,135,147,172,173,174,175,176,177,179,180,181,182,183,184,188,203,214,215,216,217,302,306,340,342,391,427]
	Others	[30,51,114,115,116,124,125,145,147,148,151,152,155,172,173,179,192,199,200,204,208,308,341,342,358,428]
Unsupervised	Clustering	[131,324,427,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445]
	SOM	[134,191,439,446,447,448,449,450,451,452,453]
	DL	[135]

. Note that (i) for brevity, acronyms represent models’ names here and full names can be found in the Nomenclature and (ii) for consistency, exemplary ‘Bst (95 times)’ is used to indicate 95 appearances of the Bst model/category in the reviewed articles, preferred over ‘Bst (95 studies)’ as many studies contained more than one model belonging to the Bst group/category.

4.1. Supervised Models

Supervised learning addresses the strategy for discovering and predicting patterns when the model is provided with both predictive and target variables [54]. This ML type consists of the most popular models that follow various linear and non-linear approaches to map the input–target relationship. A notable advantage of supervised learning is that, when sufficient labeled data is provided, the model can be satisfactorily trained and tested to achieve a reliable solution. Moreover, these algorithms are automatic, eliminating the need for the user to perform decision-making and tune too many parameters. Such advantages have driven scientists to choose supervised learning algorithms in 94% of MLGHM cases (Figure 3).

4.1.1. Artificial Neural Networks

ANNs are famous members of the ML family that follow a biological approach (human neural system) for pattern analysis. Reportedly, the idea of ANNs was first presented in Ref. [55]. In ANNs, computational units are neurons that, despite lying in different layers, are highly connected by weights (i.e., synapses) throughout the network [56]. This feature, as well as taking advantage of powerful training strategies (e.g., backpropagation [57]), training algorithms (e.g., Levenberg–Marquardt [58]), and non-linear activation functions, enables ANNs to establish an accurate mathematical relationship between the predictive and target variables. Many studies have applied ANNs to model environmental parameters such as water quality [59] and groundwater level [60].

The earliest applications of ANNs in GHM were presented by Almasri and Kaluarachchi [61] in 2005 and Wang, et al. [62] in 2006; however, scientists are still employing ANNs for this purpose. While the reviewed articles used different terminologies to refer to conventional ANNs, the models’ structures indicated that they are mostly MLP, which is known as a universal approximator [56]. The whole group of ANNs forms 14% (=88 times) of supervised MLGHM models comprising conventional ANNs (70 times), DL (11 times), and Other (7 times), which itself comprises MNN (2 times), ELM (2 times), GMDH (1 time), ELNN (1 time), and BRNN (1 time).

4.1.2. Neuro-Fuzzy Models

A neuro-fuzzy (NF) model represents a combination of two paradigms, namely ANN and fuzzy logic (FL). It results in a strong predictive tool that is able to capture non-linear input–target relationships [63]. Introduced by Zadeh [64], FL is known as a mathematical framework that deals with reasoning and decision-making and addresses uncertainty and vagueness. A strength of FL is that it uses membership functions (MFs) such as triangular, trapezoidal, and Gaussian, allowing an element to have a membership degree (e.g., 0–1) instead of belonging to binary classes (0 or 1). ANFIS [65] is the most popular NF model that is composed of five layers that are responsible for the calculations as follows: (1) Fuzzification Layer: calculating the input MFs, (2) Rule Layer: calculating the firing strength, (3) Normalization Layer: normalizing firing strength, (4) Defuzzification Layer: computing weighted outputs, and (5) Summation Layer: computing the final output [66]. It is worth explaining that the difference between ANFIS and other NFs (e.g., CANFIS, DENFIS, and HyFIS) lies in the improvements, including CANFIS using an MNN, HyFIS using an MLP with gradient descent learning, and DENFIS following continuous evolving after new data entry. Due to these merits, NF models have received significant attention in various environmental domains, including hydrology [67] and groundwater level [68].

Whilst sophisticated, NF is one of the pioneering models that was first used by Dixon [69] in 2005. NF models constitute 3% (=20 times) of supervised MLGHM models, comprising ANFIS (16 times), CANFIS (2 times), DENFIS (1 time), and HyFIS (1 time).

4.1.3. Tree-Based Models

Tree-based models form a large portion of the ML community. These models are built upon binary classification trees, in which the most significant predictive variable is positioned at the root, followed by less significant ones in the subsequent positions. Owing to advantages such as less computational cost [70] and high interpretability [71], these models have received tremendous attention in prediction efforts. RF is the most reputable tree-based model that was devised by Breiman [72] as a combination of randomized DTs. This model has successfully dealt with prediction tasks in water-related sectors [73].

The oldest representative of this group was RF, used by Rodriguez-Galiano, et al. [74] and Nolan, et al. [75], both in 2014. This group accounts for 25% (=160 times) of supervised MLGHM models comprising RF (118 times), DT (12 times), CART (10 times), ERT (8 times), M5 (4 times), and Others (8 times) that itself comprise BART (2 times), LMT (2 times), RotF (1 time), J48 (1 time), RT (1 time), and RndT (1 time).

4.1.4. Support Vector-Based Models

Proposed by Cortes [76], SVM is another competent group of ML that is built on statistical learning theory. The key concept in training SVMs amounts to defining decision boundaries by identifying reproducible hyperplanes that maximize the distance between support vectors of the class labels [77]. Strong function approximation and quick learning are strengths of SVMs that have made them popular LM models for various predictions, particularly in hydrology [78] and other environmental sectors [79,80].

Employed by Ammar, et al. [81] in 2008, RVM represented the first appearance of SVMs within the surveyed studies. This group forms 10% (=63 times) of supervised MLGHM models, consisting of SVM (49 times), SVR (12 times), and RVM (2 times).

4.1.5. Regression Models

Being among the most straightforward ML models, regression models are useful to delineate the relationship between predictive and target variables. This group possesses various linear and non-linear notions such as MLR and LgR [82] that have gained significant interest in environmental studies [83], and notably hydrological research [84,85].

The first MLGHM article that used a regression model (LgR) was published by Twarakavi and Kaluarachchi [86] in 2005. The regression family is the fourth popular ML group, accounting for 12% (=75 times) of supervised MLGHM models comprising LgR (37 times), MLR (16 times), GLMs (7 times), MARS (7 times), and Others (8 times) that itself comprise PolyR (2 times), BRR (2 times), glmnet (1 time), AFR (1 time), LsR (1), and RR (1 time).

4.1.6. Probabilistic Models

Probability theory is the essence of many ML-related rules. Depending on the used interpretation (i.e., frequentist or Bayesian [87]), different approaches can be regarded for pattern identification and uncertainty quantification in these models. In this regard, integration of simple probability distributions over (one or) a few variables forms a more complex model [88]. The ease of use and the high predictive potential of these models have made them popular tools for modeling purposes [89], including environmental predictions [90,91].

Probabilistic models have been mostly used in the last decade of the MLGHM literature, as the first application refers to using a BN model by Nolan, et al. [92] in 2015. This ML family accounts for 5% (=34 times) of supervised MLGHM models encompassing five classes of Bayesian (10 times), Gaussian (10 times), discriminant (10 times), Markovian (3 times), and Others (1 time). Among 15 unique probabilistic models, Gaussian GP (9 times) was the most popular, followed by Bayesian NB (6 times), discriminant MulDA (5 times), and discriminant LDA (3 times). Other models that appeared once include Bayesian models of BN, NBT, BMA, and BME, the Gaussian model of GCM, discriminant models of FDA and QDA, Markovian models of MMRF, CMMRF, and FMRF, as well as MaxEnt (Others).

4.1.7. Ensembles

Ensembles are another promising type of ML models that altogether form 27% (=171 times) of supervised MLGHM models. However, considering the strategies used for creating ensembles, this category is divided into two major parts:

Ensemble 1: The category is dedicated to ML models that incorporate either of bootstrap aggregating (bagging, Bag) [93], boosting (Bst) [94], disjoint aggregating (dagging, Dag) [95], and random subspace (RS) [96] techniques for performance improvement. This improvement is achieved by leveraging multiple base learners and aggregating their outputs. While Dag and Bag perform parallel training of the models toward reducing variance, Bst relies on a sequential approach that results in reducing bias. RS, on the other hand, employs techniques based on feature diversity to enhance decorrelation within base models. These models have extensively served for various purposes [97,98,99], including environmental predictions [100,101,102].

Although most Ensemble 1 models have appeared after 2020, the first application was a BRT model in Ref. [92] that was published in 2015. 19% (=121 times) of supervised MLGHM models belong to Ensemble 1 category, comprising Bst (95 times), Bag (17 times), Dag (7 times), and RS (2 times). Notably, Bst encompassed 12 different models, out of which, BRT (28 times), XGBoost (25 times), AdB (9 times), and LGBM (9 times) were the most favored ones.

Ensemble 2: Unlike Ensemble 1 models that rely on resampling techniques, the second group of ensembles represents models that are founded on synthesizing two (or more) algorithms for creating improved versions. Many scholars have successfully applied this type of ensemble to various water- and groundwater-related problems [103,104].

Considering the underlying strategy for combining models, Ensemble 2 consists of three major classes, here referred to as Groups 1, 2, and 3 (detailed below), all accounting for 8% (=50 times) of supervised MLGHM models comprising Group 1 (21 times), Group 2 (21 times), and Group 3 (8 times). The details of these groups are as follows:

(i)

Group 1: Meta-models (MMs) comprising committee and stacking learning that exhibit two-level predictions, i.e., the outputs of the models in Level 1 are considered inputs for another model in Level 2 (A.K.A. Levels 0 and 1). Fijani, et al. [105] presented the first application of such models (SCMAI) in 2013.

(ii)

Group 2: Metaheuristic optimization algorithm (MOA)-based models in which an MOA optimizes a baseline ML. MOAs are known as global optimizers that can tackle complicated problems [106,107]. These algorithms employ search operators to systematically update the solution in the search space through exploiting and exploring the knowledge. Such strategies ensure the final solution is globally optimum, i.e., protected from getting stuck in local minima [108]. The use of GA for optimizing CMAI by Fijani, Nadiri, Moghaddam, Tsai, and Dixon [105] in 2013 was the first appearance of MOAs in the surveyed literature.

(iii)

Group 3: Dual hybrids (DHs) are created by integrating two baseline ML models. These models usually deliver stronger solutions than single conventional models, due to benefiting from the computational advantages of both models simultaneously. The first representative of this group was Cubist—as a hybrid of DT and LR—used by Band, et al. [109] in 2020.

4.1.8. Others

This category accounts for 4% (=27 times) of supervised MLGHM models, consisting of instance-based learning (IBL, A.K.A. lazy learning) (18 times), evolutionary models (7 times), and physics-informed ML (PIML) (2 times), as follows:

IBL: Unlike other ML models that fit a model/function over training data and use it for prediction, IBL stores the training data and performs prediction based on similarities between the stored and new data. These models rely on distance measures such as Euclidean and Cosine distance to find stored samples that are most similar to the new data [110]. Proposed by Fix and Hodges [111], KNN is the only entity of this category that was used for MLGHM purposes. In KNN, the distance of a new point from all training data is calculated, then, a prediction takes place by focusing on the k nearest neighbour points (with k being user-defined). Earlier studies highlighted KNN’s applicability in various sectors [112], including environmental simulations [113]. Starting from 2019 in Refs. [114,115,116], KNN appeared in 18 MLGHM studies.

Evolutionary learning: Evolutionary models are inspired by the Darwinian natural selection principle, aiming to evolve the solution over generations. In these approaches, mutation, crossover, and selection processes are applied to the parent solutions to generate offspring of higher quality [117,118]. These techniques have generated immense interest in various ML studies [119,120], and more particularly, in environmental modeling [121]. GEP, which was designed by Ferreira [122], is the only algorithm of the evolutionary group found in the surveyed literature. Besides its reliable accuracy, a strength of GEP is that it can present the solution in the form of an efficient and explicit mathematical formula that is less complicated than an ANN-derived formula [123]. Nadiri, et al. [124] first used GEP for GHM in 2017. Following this, six other studies used this model, resulting in a total of 7 times of use.

PIML: The reviewed literature reflected one application of a model named U-FNOB (and its extension, U-FNOB-R) that works on the basis of the Fourier neural operator (FNO). These models are among the rarest ML models; hence, their technical details can be found in the relevant article, i.e., Ref. [125].

4.2. Unsupervised Models

Unsupervised learning addresses models that are used for finding the latent patterns/clusters within unlabeled data [126]. In other words, the model is not provided with target (or response) values attributed to the predictive variables. It rather performs clustering on data based on commonalities. It is considered an advantage of these models, enabling them to be used in semi-supervised scenarios where there is a restricted number of labeled data [127]. Unsupervised ML models have served for various predictive purposes, especially in environmental and water-related fields [128,129,130]. Unsupervised category covers 6% (=38 times) of MLGHM models (Figure 3).

4.2.1. Clustering Models

Identified clustering models comprise FCM, KMC, KMdC, HCA, and APC. Whilst all follow the clustering approach for data analysis, there are differences between them that result in pros and cons for each technique. Due to the use of FL in FCM, it can perform soft clustering, in which data points are assigned membership degrees for different clusters rather than pertaining to one. KMC has a low computational cost, while KMdC is robust to outliers due to considering medoid points (rather than centroids) as the centre of the cluster. HCA uses a tree-structured clustering, making it suitable for visualizing hierarchical relationships. APC has the advantage of automatic determination of the number of clusters.

By using a KMC by Das, et al. [131] in 2010, clustering models started gaining attention for GHM, and include 66% (25 times) of unsupervised MLGHM models comprising KMC + KMdC (12 times), HCA (7 times), FCM (5 times), and APC (1 time).

4.2.2. Self-Organizing Map

Proposed by Kohonen [132], SOM is a popular unsupervised ML that has been widely used for environmental modeling purposes. This model has an ANN-like skeleton that enables it to map high-dimensional data onto a simpler grid (mostly 2D) whilst maintaining the topological relationships [133]. The earliest appearance of SOM in MLGHM literature corresponds to Ref. [134] that was published in 2014. SOM-based accounts for 29% (11 times) of unsupervised MLGHM models, comprising single SOM (8 times), SOM combined with KMC and FCM (2 times), and GNG (1 time).

4.2.3. Unsupervised Deep Learning

Contributing to 5% (2 times) of unsupervised MLGHM models, Faal, et al. [135] used two DL models, namely DBN and DSA, in an unsupervised manner. Technical details regarding these models can be found in the cited article.

5. What Defines a Better Model?

A key aim of this review was to assess the comparative advantages and disadvantages of various MLGHM models with a view to providing guidance on optimal model selection for different users. Model selection ideally requires an understanding of both (i) what are important model selection criteria and (ii) how these various criteria should be weighted—in other words, what defines a ‘better’ model? Clearly, the weighting of various criteria may be quite subjective and may vary from problem to problem. Further, as Fisher, et al. [136] stated “All models are wrong, but many are useful”. With these limitations in mind, this section addresses several characteristics of a ‘good’ model, based on which the surveyed MLGHM models will be assessed in Section 6. Note that most of these criteria are described briefly here with further discussion in Section 8. In addition to the criteria for assessing the selection of ML models, we also consider various aspects of ML model design.

5.1. Model Design and Data Handling

(i)

Role of assumptions: Many data-driven models are able to satisfactorily learn and reproduce intrinsic non-linear patterns. There is overwhelming evidence of the suitability of ML models for exploring the relationship between GWQ and its influencing factors. But an overlooked question regarding many ML-based efforts is ’To what extent can the performance of an ML be influenced by the modeling assumptions?’

(ii)

Feature selection: As shown in Section S1.5, many MLGHM studies have benefited from feature selection to optimize the models in terms of dimensionality. These techniques can help ML models by improving learning performance, preventing overfitting, and/or reducing computational costs [137].

(iii)

Dataset adjustment: The data splitting ratio, which specifies what portions of the dataset are dedicated to the training and testing phases [39], is an important factor that can impact the quality of training, and consequently, the quality of the prediction results. In addition, data-centric cross-validation techniques (e.g., K-Fold) [138] can be regarded as addressing the stability of the model.

5.2. Model’s Performance and Reliability

(iv)

Accuracy and validation: Accuracy assessment is one of the most important steps of any modeling. In MLGHM efforts, scientists have extensively used accuracy metrics (e.g., RMSE, AUC, and R²) to validate and compare the performance of their models.

(v)

Hyperparameters (tuning and presentation): Recognizing and proper determination of models’ hyperparameters is vital as they can impact the quality of the prediction. ML models, therefore, should ideally be hyperparameter-tuned to maximize the model’s potential and to be hyperparameter-transparent to support reproducible research.

(vi)

Stability: Stability of an ML model can be defined as its ability to maintain consistent performance when exposed to small perturbations. In this sense, recognizing the sources of uncertainty, as well as assessing the models’ repeatability and ensuring the results’ reproducibility, can be helpful.

(vii)

Generalizability (transferability): overfitting can be a general threat even to models that exhibit high accuracy and can result in models not being generalizable or transferable to new (unseen) data [139,140], due to the learnt pattern being excessively specific to the training data [141].

(viii)

Explainability (transparency/interpretability): Many of the reviewed ML models lack explainability, i.e., a clear presentation of the internal processes, and so are labeled here as ‘opaque-box’ models. In contrast, explainable artificial intelligence (XAI) is an increasingly used term to describe more explainable ML models that enable human users to better understand and so better trust [142].

(ix)

Optimizability: optimizing an ML model can be conducted with respect to data and dimension, the model’s architecture, hyperparameters, and the training algorithms, and can lead to a more applicable model.

5.3. Computational Efficiency

(x)

Computation time: Particularly for models of large datasets, reducing the computation time to attain a target accuracy may be an important model characteristic [143] necessitating a computationally efficient model. This factor should be evaluated with respect to the operating system’s characteristics (e.g., RAM and CPU frequency) to reflect the models’ computational demand fairly.

(xi)

Penalizing for complexity: Penalty functions aim to address a trade-off between the model’s fitness and its complexity. To this end, the model is penalized (sometimes partly) with respect to the number of its computational parameters (e.g., the number of intercepts, coefficients, and error variance in MLR).

5.4. Practical Application

(xii)

Informed hazard zonation (IHZ): Once a GHM is produced, it is essential to correctly classify the study area into different hazard classes for optimizing decision-making and cost estimations. Popular methods for doing so are based on statistical methods (e.g., Equal Intervals) and/or regulatory standards; however, more recent studies explicitly consider model accuracy and purpose-related model-informed cost-benefit balances.

6. Machine Learning Models—Comparative Assessment

This section provides an extensive comparison of the reviewed MLGHM models utilising ‘better model’ metrics beyond just model accuracy [38,39,40,41]. Due to the shortage of adequate evidence for the relative assessment of unsupervised models, this section focuses on supervised MLs and, in particular, considers those reviewed MLs from articles that were more comprehensive and informative

Table 1. Multi-criteria comparison of selected reviewed MLGHM models.

L.	Reference	Target Parameter	Country	Models (Most Accurate > Others)	Criteria Considered
					Data Adjustment			Hyperpa.		Comp. Efficiency			Others/Comments
					TSR	CV	FS/IA	Opt	Rep	CT	OS	PF
A	Khan and Ayaz [144]	WQI	India	ANN > MLR, GP, SVM, RT, BRT			★✖						- Addressing uncertainty
	Esmaeilbeiki, et al. [145]	H, EC	India	DENFIS, GEP > GMDH, MARS, M5			✖						- Considering input scenarios
	Kerketta, et al. [146]	F−	India	ELM > XGBoost, SVM, RF, ANN		✖	✚	⃞  ✔✖	✔				- POF by various inherent features - Using MOAs (GA) for model optimization
	Boudibi, et al. [147]	Salinity (EC)	Algeria	RF > HyFIS, KNN, Cubist, SVM		✔	✖	✖	✔
	Khiavi, et al. [148]	WQI	Iran	RF > NB, SVM, KNN			★✔						- Using game theory for model assessment
	Javidan and Javidan [149]	${\mathrm{N}\mathrm{O}}_3^{-}$	Iran	CMMRF > RF, MMRF, FMRF			✖						- Using cutoff-dependent accuracy metrics - Briefly discussing transferability
	Tavakoli, et al. [150]	RI (TDS)	Iran	RF > BRT, SVM, MARS, GLM					✔				- Briefly discussing transferability
	Chahid, et al. [151]	VI (${\mathrm{N}\mathrm{O}}_3^{-}$)	Morocco	ERT > BA, ANN, KNN			✖	✖	✔				- Using evolutionary algorithms for model optimization - POF by various inherent features
	El-Rawy, et al. [152]	WQI	Egypt	RR > RF, XGBoost, DT, KNN			★✖❄					✔	- Considering input scenarios - POF by various inherent features
	Liang, et al. [153]	${\mathrm{N}\mathrm{O}}_3^{-}$	China	RF > XGBoost, SVM		✔	O	⃞					- Using SHAP to address explainability - POF by XGBoost’s inherent features - Addressing uncertainty by statistical analysis
	Bordbar, et al. [154]	SWI, WQI	Italy	RF, SVM > BRT			✖✔						- Briefly discussing transferability
	Bakhtiarizadeh, et al. [155]	${\mathrm{N}\mathrm{O}}_3^{-}$	Iran	GEP, GA-PolyR > PSO-MARS, M5		✔	✚	✖	✔	✔			- POF by various techniques - Discussing explainability
B	Díaz-Alcaide and Martínez-Santos [116]	Fecal cont.	Mali	RF > LgR, ANN, SVM, DT, KNN, LDA, NB, AdB, QDA, GBC, GP	✔		✚	⃞		⃟			- Ensembling the elite models - Addressing uncertainty - Briefly discussing transferability and explainability
	Liang, et al. [156]	${\mathrm{N}\mathrm{O}}_3^{-}$	China	GBR > RF, XGBoost, AdB		✔	✔★	⃞  ✖					- POF by XGBoost’s inherent features - Addressing uncertainty using PICP and MPI
	Sarkar, et al. [157]	Salinity (EC)	India	RF > GBoost, LgR		✔	▲✖ ✔★	✖	✔				- Using DSRM to address the issue of imbalanced data - IHZ using cutoff point - Addressing transferability by large-scale modeling
	Tran, et al. [158]	Salinity (Cl−)	Vietnam	CatBoost > RF, XGBoost, LGB		✔	✔	⃞	✔	⃟		✔	- GHM classified based on WHO standards - Superior model achieved lowest penalty and fastest training
	Huang, et al. [159]	${\mathrm{N}\mathrm{O}}_3^{-}$	China	XGBoost > CART, GBM, RF, LGBM		✔	O✔	✖	✔				- Using SHAP to address explainability - POF by XGBoost’s inherent features
	Aju, et al. [160]	WQI	India	RF > XGBoost, SVR, ANN			O	✖					- POF by XGBoost’s inherent features - Using SHAP to address explainability
	Barzegar, et al. [161]	TDS	Iran	XGBoost > R, LGBM, AdB, CatBoost		✔	★	⃞	✔				- POF by XGBoost’s inherent regularization - Addressing reproducibility
	Tachi, et al. [162]	${\mathrm{N}\mathrm{O}}_3^{-}$	Algeria	CatBoost > AdB, RF			★✔						- POF by various inherent features
	Knoll, et al. [163]	${\mathrm{N}\mathrm{O}}_3^{-}$	Germany	RF > BRT, CART, MLR		✔	✚	✔	✔			✔	- Using stratified random sampling for data division - POF by various inherent features - Briefly discussing transferability - Addressing transferability by large-scale modeling
	Pal, et al. [164]	${\mathrm{N}\mathrm{O}}_3^{-}$	India	Bst > Bag, RF		✔	✔	✔	✔				- POF by various inherent features
	Sun, et al. [165]	${\mathrm{N}\mathrm{O}}_3^{-}$	China	Bag > Bst, GBDT, RF, SVM, ANN,		✔	★O✔						- POF by various inherent features - Using SHAP to address explainability
	Bordbar, et al. [166]	VI (TDS)	Iran	BA-LMT > DA-LMT, BA-NBT, DA-NBT, RS-NBT, RS-LMT, LMT, NBT									- POF by various inherent features
	Islam, et al. [167]	${\mathrm{N}\mathrm{O}}_3^{-}$	Bangladesh	Bst > Bag, RF		✔	✖	✔	✔				- POF by various inherent features
C	Singha, Pasupuleti, Singha, Singh, and Kumar [46]	WQI	India	DL > XGBoost, ANN, RF	✔	✔	✚	⃞  ✔✖	✔				- POF by Dropout, mini-batch size, and L2 regularization
	Meng, et al. [168]	RI (${\mathrm{N}\mathrm{O}}_3^{-}$)	China	DL > RF, ANN		✔	✚						- Stability analysis by coefficient of variation - Assessing prediction symmetry by OEE/UEE
	Gholami and Booij [169]	${\mathrm{N}\mathrm{O}}_3^{-}$	Iran	XGBoost > DL, MLR			★✔	✔	✔				- POF by XGBoost’s inherent features
	Kumar and Pati [170]	As	India	DL > XGBoost, RF, GBM, DT, NB			★	⃞	✔
	Karimanzira, et al. [171]	${\mathrm{N}\mathrm{O}}_3^{-}$	Germany	RF > various DLs		✔	▲✔	✖	✔	✔	✔		- Using leave-one-out encoding technique - POF in DL using Dropout technique - Addressing uncertainty using PICP and MPIW - Briefly discussing transferability - Addressing explainability - Superior model achieved fastest training
D	Li, et al. [172]	${\mathrm{N}\mathrm{O}}_3^{-}$	England	KNN-SEL > GBDT, XGBoost, RF, ERT, KNN		✔	★O	✖	✔				- Ensembling using KNN - Using SHAP to address explainability - Addressing stability and generalizability through CV - Superior model achieved better generalizability and stability
	Cao, et al. [173]	As, F−	China	LDA-SEL > RF, ERT, DT, XGBoost, AdB, GBDT, SVM, KNN, LDA, LgR, ANN		✔	✖						- Ensembling using LDA - Using optimal entropy-weighted to select SEL components
	Moazamnia, et al. [174]	VI (Salinity)	Iran	SVM-AIMM > ANN, NF				✔					- Ensembling using SVM
	Nadiri, Gharekhani, Khatibi, Sadeghfam, and Moghaddam [124]	${\mathrm{N}\mathrm{O}}_3^{-}$	Iran	ANN-SICM > SVM, NF, GEP				✔	✔				- Ensembling using ANN - Yielding an explicit formula from GEP - Dividing study area into three parts due to heterogeneity
	Bordbar, et al. [175]	VI (SWI)	Iran	ANN-SCMAI > NF, SVM, ANN				✔	✔				- Ensembling using ANN - Assessing statistical significance of models’ differences by Friedman’s and WSR tests
	Fijani, Nadiri, Moghaddam, Tsai, and Dixon [105]	VI (${\mathrm{N}\mathrm{O}}_3^{-}$)	Iran	ANN-SCMAI > ANN, ANFIS,		✖		✔	✔				- Ensembling using ANN - Using MOA (GA) to train the ensemble model
	Barzegar, et al. [176]	RI (${\mathrm{N}\mathrm{O}}_3^{-}$)	Iran	ANN-Committee > SVR, M5 Tree, ELM, MARS			✖	⃞ ✔✖	✔		✔	✖	- Ensembling using ANN - POF by various inherent features - Briefly discussing explainability
	Barzegar, et al. [177]	VI (${\mathrm{N}\mathrm{O}}_3^{-}$)	Iran	ANN-SCMAI > ANN, NF		✖		✔	✔				- Ensembling using ANN - Using MOA (GA) to train the ensemble model
	Jafarzadeh, et al. [178]	${\mathrm{N}\mathrm{O}}_3^{-}$, TDS	Iran	AdB-Ens > AdB, XGBoost, LGBM, RF		✔		⃞	✔				- Ensembling using AdB - POF by various inherent features - Performing holistic GVM by integrating DRASTIC and GALDIT
	Faal, Nikoo, Ashrafi, and Šimůnek [135]	Salinity (TDS)	Iran	GP-Ens > SVR-Ens, ANN-Ens, DNN, CNN, DBN, DSA				✔	✔	✔			- Ensembling using GP, SVR, ANN - POF by various inherent features - Superior model achieved fastest training
	Usman, et al. [179]	F−	Africa	NB-SEL > LgR, DT, RF, SVM, NB, KNN, AdB, XGBoost, LGBM, CatBoost, GBDT, BA-DT, ANN, ERT, LDA		✔	✖						- Ensembling using NB - Briefly discussing transferability - POF by various inherent features - Addressing transferability by large-scale modeling
E	Jamei, et al. [180]	Salinity	Bangladesh	ANFIS-AO > ANFIS-SMA, ANFIS-ACO, LsR, ANFIS,			✔	✔ ⃞	✔		✔		- Addressing uncertainty by U95% - POF by Monte Carlo technique - Using MOAs (AO, ACO, SMA) for model optimization - Considering input scenarios
	Elzain, et al. [181]	VI (${\mathrm{N}\mathrm{O}}_3^{-}$)	S. Korea	ANFIS-PSO > ANFIS-DE, ANFIS-GA, ANFIS	✔		★	✔	✔	✔			- Using various MOAs for model optimization - Superior model achieved fastest training (amid MOAs) - Briefly discussing transferability
	De Jesus, et al. [182]	Cr, Cd, Fe, Mn, Zn, Ni, Pb, Cu	Philippines	PSO-ANN > SVM, MLR			★✖	✔	✔	✔		✔	- Using MOAs (PSO) for model optimization - Using KGE for model assessment - POF using early stopping approach
	Pham, et al. [183]	${\mathrm{N}\mathrm{O}}_3^{-}$	Vietnam	RF-FA > RF-MOE, RF-Ant, RF-GWO, RF-PSO, RF			★		✔	✔			- Using various MOAs for model optimization - Briefly discussing transferability - Superior model achieved fastest convergence (amid MOAs)
	Saha, et al. [184]	VI	India	RF-GOA > RF-GWO, RF-PSO, RF			❄✔★		✔				- Using various MOAs for model optimization - Briefly discussing transferability

Notes: Legend: Heads => L: Label, Ref: Reference, Loc: Location. Data Adjustment => TSR: Testing Splitting Ratios, CV: Data Cross-Validation, FS/IA: Feature Selection/Importance Assessment. Hyperparameters => Hyperpa: Hyperparameters, Opt: Optimization, Rep: Report. Comp. Efficiency => CT: Computation time, OS: Operating System, PF: Penalty Function. Ensemble Models => X-Ens: Ensembled using X model. CV => ✔ K-fold, ✖ Not Stated. FS/IA => ✔ Tree-based, ★ Correlation, ✚ Multiple, O SHAP ❄ PCA, ▲ PDP, ✖ Others. Opt => ✔ T&E, ⃞  GS, ✖ Others/Not Stated. CT => ✔ Quantitatively, ⃟  Qualitatively. PF => ✔ AIC and/BIC, ✖ Others.

summarizes the information extracted from 46 selected articles. While all studies performed reliable accuracy assessment using several popular metrics (e.g., RMSE, MAE, AUC, R²) that mostly resulted in explicitly distinguishing one model as superior, not all of them provided an explicit ranking of the used models. For conciseness, both in Table 1 and throughout the text, “>” and “<“ are used to indicate that the first model is more accurate or less accurate, respectively, than the second model. Most of the reviewed papers provided a firm scientific background and assumptions to conduct MLGHM. Assessment of these assumptions is discussed in Section 8.

The studies are divided into five categories labeled as follows:

• Label A focuses on comparing mostly conventional models, including (but not limited to) ANNs, NFs, SVMs, and simple tree-based models,
• Label B focuses on the competition between tree-based and Ensemble 1 models,
• Label C addresses the competency of DL, asserting itself as a competitive model to the above two groups,
• Label D focuses on MM ensembles (Ensemble 2—Group 1),
• Label E evaluates MOA-based ensembles (Ensemble 2—Group 2) versus relevant baseline models.

Some further features of MLs are outlined below:

(i)

Data Adjustment: Many studies considered feature selection (and/or importance assessment) using popular models (e.g., tree-based MLs, PDP, and PCA) to delineate the role of predictive variables. As an interesting idea, some studies (e.g., Refs [145,180]) created and imposed various combinations of predictive variables that led to identifying the most accurate prediction scenarios. Many works also took advantage of data-centric cross-validation (mostly the K-fold technique) as part of data adjustment. Nevertheless, a few studies (e.g., Refs. [46,116]) paid attention to optimizing the data splitting ratio that reportedly can be an accuracy-determinant factor.

(ii)

Hyperparameters: Reporting the used hyperparameters was inconsistent, i.e., present in many articles but missing in many others. Most studies, however, benefit from automatic methods such as the GS algorithm and manual methods such as T&E to ensure proper assignment of hyperparameters.

(iii)

Computational efficiency: Some studies considered documenting computational details (e.g., computation time [135,155,171,182,183] and the used operating system [171,176,180]). These two factors can reflect important information regarding an informed selection of efficient MLs, due to the complexities of some MLs and occasional limitations in computer facilities. Moreover, utilizing penalty functions to constrain the model’s complexity is another promising direction for proper selection of the model (and predictive variables). However, it was observed in a small portion of the surveyed articles (e.g., Refs. [152,158,163,182]). To exemplify, in Refs. [135,171], the outstanding model not only achieved the highest accuracy, but also was quicker in terms of training time (and convergence of the solution [183]). Further, Ref. [158] indicated that its superior model achieved these merits along with the lowest penalty expressed by AIC and BIC.

(iv)

Others: Many studies leveraged internal and external techniques (e.g., XGBoost’s inherent regularisation [159] and Dropout for DL [171]) to prevent overfitting. In contrast, quantitative evaluation of prediction uncertainty was explored in a few studies (e.g., using statistical indices of PICP [156] and U95% [180]). Models’ explainability, generalizability, and results’ reproducibility likewise received limited attention, as they were often discussed in brief. Last but not least, IHZ remained almost underexplored despite its great importance. The vast majority of the reviewed studies employed well-established methods (e.g., natural breaks, equal hazard interval, and WHO standards) to classify the studied aquifers in terms of hazard. Only a few studies (e.g., Ref. [157] from Table 1 and others [185,186,187]) identified AUC-based cutoff optimization for determining hazardous areas.

6.1. Accuracy Comparison

6.1.1. Label A

This category provides evidence of the high ability of various conventional MLs that outperformed each other and even ensemble models.

ANNs: Various ANNs, including MLP [144], DL [170], and ELM [146], were found to be more powerful than other MLs. The MLP used in Ref. [144] also exhibited lower uncertainty than SVM, MLR, RT, GP, and BRT.

NFs: ANFIS surpassed (non-ML) FLs, including Mamdani and Sugeno [174,177], reflecting the positive contribution of the neural system that is embedded in this model (See Section 4.1.2). In Refs. [175,188], ANFIS stood in a close competition with ANN and SVM, whereas it was outperformed by them in Refs. [124,189,190]. Modified versions of ANFIS, however, mostly provided better accuracy than different MLs. In this regard, CANFIS [191] and DENFIS [145] were more accurate than SOM, ANN, GEP, GMDH, MARS, and M5, while HyFIS [147] showed weaker results than RF and SVM.

Tree-based models: These models—and on top of them, RF—came up with higher accuracy than a wide variety of MLs in many comparative studies. In Ref. [116], RF achieved the most balanced set of accuracy metrics when it was in competition with LgR, ANN, SVM, DT, KNN, LDA, NB, AdB, QDA, GBC, and GP. Similarly, Ref. [192] revealed the greater accuracy of RF over SVM, XGBoost, KNN, ANN, and GCM. Agreeable outcomes can be found in other studies, such as Refs. [148,150,165,193]. As for other tree-based models, several efforts demonstrated the superior accuracy of ERT [151], BART [194], and CART [195] versus diverse ML competitors.

SVMs: Despite possessing several advantages, viz., high speed, reliability, and cost-effectiveness for GHM [196], SVMs appeared frequently as benchmark models. SVMs showed promising performance, providing higher accuracy than popular MLs, viz., MulDA, BRT, and GLM [197], RF and BRT [154], and ANFIS [190]. SVR is a relatively more powerful member of this family that was found to be more accurate than MLs, including RF and SVM [198], RF [199], KNN [200], MARS and GLM [150], and ANN [201].

Regression models: Conventional versions of regression models have rarely been dominant in the MLGHM literature. MARS once appeared to be the most accurate model, outperforming SVM, MDA, GLM, and GBM in Ref. [202]. Also, Ref. [150] gives an example of its higher accuracy compared to GLM. RR is a potent regression model that, in Ref. [152], ranked higher than RF, XGBoost, DT, and KNN accuracy-wise. LgR that was used in Ref. [116]—yielding a comparable performance with RF—was more accurate than SVM, GP, and ANN. Moreover, GLM exhibited higher accuracy compared to FDA in Ref. [203].

Probabilistic models: Multiple advantageous applications of probabilistic models have put them among successful MLs in the surveyed literature. Researchers suggested GHM uncertainty evaluative techniques through Bayesian frameworks of BMA [204] and BME [205]. In Ref. [204], this idea resulted in the superior accuracy of BMA versus ANN, GEP, and SVM. GP is another powerful probabilistic model that showed higher accuracy compared to RF and ELNN [206], as well as (non-ML) kriging models [207]. Another notable application of probabilistic models was carried out in Ref. [149] using CMMRF that surpassed RF in terms of prediction accuracy.

Others: While KNN was mostly used as a comparative benchmark for more sophisticated models [114,208], there are a few studies quantifying the relative merits of this model. For instance, KNN’s accuracy was found to be higher than that of LDA and QDA in Ref. [116] and higher than ANN and GP in Ref. [192]. Regarding GEP, its accuracy-wise excellence was identified in Ref. [145], surpassing that of M5Tree, MARS, GMDH, and DENFIS, and in Ref. [155], outperforming M5 and two MOA-tuned models of GA-PolyR and PSO-MARS.

6.1.2. Label B

The use of resampling techniques, including Bag, Bst, Dag, and RS, has resulted in significant improvements in many MLs. For instance, Ref. [166] showed that the baseline models of LMT and NBT experience higher accuracy once they were incorporated with Bag, Dag, and RS techniques. Similar improvement was attained for RF, XGBoost, LGBM, AdB, and CatBoost by incorporating Bag and Dag in Ref. [161]. Moreover, a subset of literature highlights the greater accuracy of these techniques against conventional MLs, viz., Bag, Bst > RF [164,167], Bag, Bst > RF, SVM, ANN [165], Bag > ANN, KNN [151].

Ensemble 1 models appeared to be more powerful than several MLs, viz., BRT > SVM, MARS, GLM [150], XGBoost > DL, MLR [169], GBDT > SVM, ANN [165]. As far as the comparison among Bst models is concerned, the accuracy ranking varies across the literature. For example,

(i)

XGBoost > LGBM, AdB, CatBoost in Ref. [161],

(ii)

XGBoost > GBM, LGBM in Ref. [159],

(iii)

CatBoost > XGBoost, LGBM in Ref. [158],

(iv)

CatBoost > AdB in Ref. [162],

(v)

AdB > XGBoost, LGBM in Ref. [178],

(vi)

GBR > XGBoost, AdB in Ref. [156].

In addition, there is contradictory evidence suggesting both superior and inferior results of Bst models against RF. More precisely,

(i)

RF < XGBoost [158,159], BRT [209], GBR/GBM [156,159]), AdB [162], CatBoost [158,162],

(ii)

RF > XGBoost [152,153,156,157,160], BRT [150,163], GBC [116], AdB [116,156], LGBM, CatBoost [161].

From these comparisons, it can be said that Bst models show high sensitivity to the problem conditions. It, therefore, calls for assessing various Bst models—along with RF—to disclose a reliable problem-dependent solution. As a useful external (non-GHM) study, Ref. [210] sheds light on the relative performance of these models.

The potential of the discussed resampling techniques (i.e., Bag, Bst, Dag, and RS) has been comparatively evaluated in several studies as follows:

(i)

Bag > Dag > RS (applied to LMT and NBT) in Ref. [166],

(ii)

Bag > Dag (applied to RF, XGBoost, LGBM, AdB, and CatBoost) in Ref. [161],

(iii)

Bst > Bag in Refs. [164,167],

(iv)

Bag > Bst [165].

It is worth highlighting that in Ref. [161], the simultaneous inclusion of Bag and Bst techniques (in the Bag-XGBoost model) resulted in an outstanding accuracy. Although more investigations may be required to be conclusive, this paragraph suggests that Bag and Bst presented stronger predictions than the other two. Further insights regarding the comparative potential of Bag and Bst can be found in external (non-GHM) studies such as Ref. [211].

6.1.3. Label C

While DL’s performance was found to be more promising than various conventional MLs (e.g., SVM [212], DT, and NB [170]), there are still some ambiguities regarding its conclusive robustness against powerful models, including shallow ANN, RF, and ensembles.

Refs. [46,168,212] provided evidence to support a considerably higher accuracy of DL than conventional ANN. In contrast, Ref. [213] proved otherwise, i.e., (GP and) ANN outperforming DL. Moreover, Ref. [168] reported that while the used DL achieves higher accuracy, its stability—expressed as the coefficient of variation of accuracy metrics—is significantly lower than ANN. Hence, the choice between deep and shallow ANNs for MLGHM may remain a challenge that calls for more comparative efforts.

Concerning the performance of DL vs. RF, Refs. [46,168,170] reported the higher accuracy of DL, whereas Ref. [171] showed RF performs more accurately than different DLs (unimodal 2D and 3D versions). Therefore, it can be said that while DL has emerged to be a serious opponent to RF, its superiority is still ambiguous and requires further assessment.

In the surveyed literature, XGBoost and GBM were the only ensemble models that were assessed against DL. In Refs. [46,170], DL exhibited higher accuracy than XGBoost and GBM, while it was outperformed by XGBoost in Ref. [169]. Hence, similar to RF and ANNs, the evaluation of DL against ensemble models requires more evidence. It should be additionally noted that ensemble models were represented by only two Bst models in this comparison. Thus, ideally, they should be accompanied by other ensembles (other Ensemble 1 members and Ensemble 2 MLs) toward reaching reliable concluding remarks.

6.1.4. Label D

MMs that can be built upon both conventional MLs (e.g., KNN [172], NB [179], and ANN [175]) and sophisticated MLs (e.g., AdB [178]), offered improvements in GHM by outperforming several powerful models, as listed below:

(i)

KNN-SEL > GBDT, XGBoost, RF in Ref. [172],

(ii)

LDA-SEL > RF, ERT, DT, XGBoost, AdB, GBDT in Ref. [173],

(iii)

AdB-Ens > AdB, XGBoost, LGBM, RF in Ref. [178],

(iv)

GP-Ens, SVR-Ens > ANN-Ens, supervised and unsupervised DLs in Ref. [135],

(v)

NB-SEL > RF, AdB, XGBoost, LGBM, CatBoost, GBDT, BA-DT in Ref. [179].

Different from the above studies, two ensemble approaches were created by averaging the predictions of several MLs at pixel-scale (normal mean in Ref. [116] and AUC-weighted mean in Ref. [203]). While the ensemble used in Ref. [203] demonstrated superior accuracy compared to FDA, SVM, and GLM, the one in Ref. [116] was considered comparable to LgR, RFC, QDA, ANN, and SVM. Moreover, SCFL—in the position of an ANN-Ens—was used thrice in Refs. [214,215,216]. Notwithstanding this model achieving high-quality results, these three studies only used (non-ML) FL techniques for comparison. Hence, SCFL’s competency relative to other MLs remains unassessed.

Altogether, this section suggests that utilizing ML-based MMs not only provides reliable solutions for GHM but also can result in improving the accuracy of reputable MLs (e.g., Ensemble 1, RF, and DLs).

6.1.5. Label E

Several studies proved the proficiency of MOA-based ensembles mostly in comparison with the corresponding original (standalone) MLs. For instance, these comparisons

(i)

ANFIS-PSO, ANFIS-DE, ANFIS-GA > ANFIS in Ref. [181],

(ii)

ANFIS-AO, ANFIS-SMA, ANFIS-ACO > LsR, ANFIS in Ref. [180],

(iii)

RF-FA, RF-MOE, RF-Ant, RF-GWO, RF-PSO > RF in Ref. [183],

(iv)

RF-GOA, RF-GWO, RF-PSO > RF in Ref. [184],

(v)

ANN-PSO, ANN-GWO > ANN in Ref. [217],

(vi)

PSO-ANN > SVM, MLR in Ref. [182].

This suggests that synthesizing appropriate MOAs with conventional MLs such as ANN, RF, and ANFIS can result in higher accuracy. However, this section gives two important reflections regarding the comparative proficiency of MOA-based models:

(i)

The effectiveness of MOAs varies across studies (e.g., PSO being strongest in Refs. [181,217] and weakest Refs. [183,184]),

(ii)

Since each study considers only one baseline ML (ANN/ANFIS/RF), cross-category comparisons are required to assess the power of a given MOA in optimizing different baseline MLs in the same study, e.g., ANN-PSO vs. ANFIS-PSO vs. RF-PSO.

6.2. Overall Comparison

The above evaluations demonstrate that accuracy-based ranking of MLs (except for MMs) can vary from one study to another. This arises because model accuracy may be a material function of a multitude of factors (e.g., scale of modeling, data representativeness, computational artefacts, and algorithm-specific settings coupled with the operator’s influence) [41].

Further, even for well-known MLGHMs such as RF and Bst models, their computational merits have not always protected them against issues such as overfitting. In this regard, RF and GBDT that were used in Ref. [165] attained strong training and presented comparably poor test results. Supporting this, an external (non-GHM) multi-dataset evaluation of Bst ensembles in Ref. [211] showed that their performance can largely depend on the imposed datasets. Likewise, DL showed a weak performance in Ref. [213] that was attributed to the lack of large-scale balanced data with a fixed time series.

Further distinctions between MLs are considered below:

Performance and reliability: It was observed that most conventional MLs can be outperformed by more sophisticated ones. Based on Table 1, the incorporation of in-built data optimization and regularization strategies for harnessing overfitting can be two major reasons for the better performance of the latter group. RF can handle prediction tasks even when the predictive variables outnumber the samples in a dataset [218]. Besides, this model has a global reputation for in-built feature selection [219] and relative robustness to outliers and noise [72,220]. DLs, on the other hand, can benefit from the dropout strategy to regularize the training and avoid overfitting [221]. Similarly, there is an inherent use of L1 and/or L2 regularization techniques in ensembles such as LightGBM and XGBoost. Stacking and MOA-based ensembles also take advantage of multiple algorithms to protect MLs against undesirable computational phenomena.

All in all, whilst barriers such as insufficient concrete evidence and existing counterexamples precluded this study from introducing specific consistently top-performing MLs, it was witnessed that RF, DLs, and most ensembles tend to provide more accurate results than many standalone MLs, including (but not limited to) SVMs, regression models, probabilistic models, KNN, and shallow ANNs.

Complexity: The complexity of MLs is usually addressed through several criteria encompassing structure, the number of hyperparameters, and explainability, among others. Since these (currently) examinable factors are interrelated, this section discusses them together. Relying on explainability [222], it varies across various groups of MLs. Simple models, such as MLR, LgR, DT, and NB, are often listed as intrinsically explainable, while more complicated ones, including ANNs, RF, SVMs, and ensembles, are referred to as opaque-box. Not surprisingly, these opaque-box models often possess more complicated structures and a larger number of hyperparameters compared to explainable ones [223]. Also, it must be acknowledged that the degree of complexity may vary among the models that pertain to the same group. Take DLs and RF, both being opaque-box, DLs are among the most complex MLs [222], whose performance largely depends on hyperparameters; RF, on the other hand, has a few key hyperparameters leading to a lower dependency on hyperparameters [224]. As for ensembles, it can be different for each group. Whilst the complexity of MM and DH ensembles is contingent upon the applied MLs, the need for hyperparameter tuning is well-established for many MOAs [225] and Bst models [210].

The key takeaway from this section is that most promising MLs are characterized by high degrees of complexity. Referring to earlier accuracy assessments, these more complex models tend to offer a higher accuracy than simpler MLs. However, the use of RF can be considered when a favorable complexity-accuracy trade-off is required.

Computation time: As with the above factors, the computation time of a model can vary based on the problem conditions and the model’s complexity. Albeit, based on the MLGHM articles that included the model’s training time, as well as a number of external studies (e.g., Refs. [226,227,228,229]), a tentative (and prone-to-exceptions) classification of well-known MLs in terms of training time can be expressed as:

(i)

Very Fast to Fast: MLR, LgR, DT, ERT, KNN, and LDA.

(ii)

Moderate to Slow: RF, NFs, shallow ANNs, SVMs, Ensemble 1, and M5.

(iii)

Slow to Very Slow: GP, DLs, and MOA-based models.

In Ref. [210], RF was found to be slower than two ensembles of LightGBM and XGBoost, and in Ref. [171], it appeared to be over 100 times faster than a 3D DL.

In a nutshell, this section outlined several strong MLs (e.g., RF, NFs, shallow ANNs, SVMs, Ensemble 1 models) with a relatively reasonable training time that can be considered more efficient compared to heavy models such as DL and MOA. The advent of fast graphics processing units (GPUs) [230], however, indicates the precedence of accuracy over computational efficiency in assessing the relative merits of MLGHM models.

7. Informed Model Selection

This section provides a framework for selecting better MLGHM models from diverse options. Figure 4 illustrates the suggested flowchart that considers several criteria, including relative accuracy, scale of interest, and complexity (as a function of transparency, computation speed, and the number of hyperparameters, with respect to the operators’ expertise). The framework is based on the general characteristics of models, but can be prone to exceptions.

In Figure 4, the models with less complexity can be labeled as transparent-box and are generally faster. Amongst those with superior accuracy, LgR and KNN have been more used for large-scale modeling, whereas DT may offer greater utility for small-scale modeling (see Table S3 and Figure 3). Concerning MLs with moderate complexity and speed, RF has been the most popular model in both global- and local-scale predictions. In this regard, Figure 3 shows the extensive use of RF for many small-scale modelings, whereas Table S3 shows several applications of this model for supernational scales, e.g., RF by Araya, et al. [231] for salinity prediction in the Horn of Africa and by Podgorski and Berg [7] for global arsenic modeling. Other promising models, including shallow ANN, NF, SVM, and ERT, can be regarded mainly for small case studies. As for the third group, i.e., opaque-box and slower MLs, scientists have used mostly Bst (GBMs) and MM (stacking) for broad GHM, while hybrids, DLs, and MOA-based models can be good candidates for local investigations (see Table S3 and Figure 3). Overall, promising models of the first group (transparent-box and fast) can attract the attention of researchers who aim at employing lighter and simpler-to-interpret MLs. Moreover, due to the more straightforward coding and lower number of hyperparameters of these models, they demand less coding knowledge. The models in the second group (moderate transparency and speed) may require more effort to be implemented optimally, but they usually provide desirable accuracy-complexity trade-offs. Hence, they can be preferred for modeling in average circumstances. The models in the third group (opaque-box and slow), on the other hand, can mostly provide efficient modeling once executed by experienced operators via powerful computers.

8. Discussion, Conceptual Framework, and Future Work

8.1. Conceptual Framework

Optimizing MLGHM depends not only on ML model selection but how the ML is implemented. Based on the identified research gaps, this section leverages deeper discussions of the MLGHM assessment criteria (Section 5) to yield a framework that can support steps toward achieving ‘better’ modeling. Figure 5 shows this framework, suggesting the incorporation of important yet sometimes overlooked steps throughout the modeling. Explanations regarding each stage are presented, combined with the discussion in the following sections.

8.1.1. Stage 0

Role of assumptions: Scorzato [232] states that the concept of assumption-free predictions is a fallacy. Here are some important (from well-studied to partially considered to be largely overlooked) aspects regarding model assumptions that need to be checked during model design, data preparation, and implementation:

(a)

Spatial heterogeneity of data: How does the model deal with the heterogeneous distribution of the relationship between target and predictor variables? For large study areas, a possible solution can be found in Ref. [124] wherein the study area was partitioned into three sub-domains to account for the area’s heterogeneity.

(b)

Temporal variations (upon occurrence): How does the model account for temporal changes in contaminant concentrations and environmental conditions? Performing separate seasonal assessments (as in Ref. [233]) and considering temporal predictive variables (e.g., precipitation and temperature seasonality, as in Ref. [234]) may help address this issue.

(c)

Data quality and representativeness: To what extent can the provided dataset represent the sampling frame in the study area? Proper selection of predictive variables can assist the model in obtaining a deeper understanding of the relationship between contaminant and environmental conditions. For instance, aquifer dynamics can be expressed in terms of both physical and chemical characteristics [235], necessitating the inclusion of predictive variables such as time-dependent flow and water pH. Moreover, testing for multicollinearity in the data can address another significant question: Does each factor effectively (and independently) represent an aspect of the problem? Removing unnecessary factors can improve model stability and interpretability.

(d)

Problem’s non-linearity: How to ensure the model can capture any non-linear dependency of a contaminant target variable on various factors simultaneously? Comparing the accuracy of the candidate ML models to benchmark linear models (e.g., MLR in Ref. [163]) can reflect the relative capability of the models in handling MLGHM non-linearities. Plus, some linear models have pre-implementation conditions to be satisfied (e.g., ensuring the normal distribution of the target variable when using MLR).

(e)

Model verification: How to ensure a satisfactorily trained model has been protected against undesirable phenomena such as local minima and overfitting? (See Table 1).

Based on these questions, it can be said that analysing a dataset via a powerful ML model—even one achieving a high accuracy—does not necessarily guarantee results that may accurately reflect actual physical processes or have a satisfactory predictive power beyond the area for which data are available. Proper consideration of assumptions and recognizing sources of uncertainties and possible biases [236] can be of great help in model evaluation, which may also require integration of geochemical, environmental, and data science expert knowledge.

8.1.2. Stage 1

Feature selection: Most feature selection techniques (e.g., PCA and RF) follow strong statistical principles to assess the importance of predictive variables. However, for a given dataset, different feature selectors can yield different results. For instance, while PCA works based on explaining the variation of the target parameter by the predictive variables [237], the tree-based approaches reflect a decline in accuracy caused by permutations in the predictive variable [219]. For this reason, trying different feature selection techniques to achieve optimal combinations of predictive variables can be useful. However, applied feature selection methods can be unstable. For example, Mahanty, et al. [238] showed that excluding a single water quality factor from the PCA method can result in up to a 60% change in the WQI score. They suggested the use of Monte Carlo resampling and cross-validation to assess the PCA’s stability.

Splitting ratio: Two ratios of 70/30 and 80/20 are widely used for splitting ML datasets into training and testing datasets. However, a more deliberate selection of the splitting ratio is advisable, as the optimal ratio can vary from one problem (and/or one model) to another. An example of splitting ratio-centric sensitivity analysis can be found in Figure 5 and Table 6 of Ref. [116].

Cross-validation: Many ML studies rely upon a single and random split of the training and testing data, which can make the model vulnerable to performance overestimation. More clearly, spatial autocorrelation coupled with the possible unequal distribution of extreme values within the training and testing subsets can reduce the model’s accuracy. This flaw may lead to an unreliable conclusion about the model’s performance in dealing with real-world unseen extreme conditions. Data-centric cross-validation can replace the random splitting policy to secure the model against such risks. K-fold cross-validation [239] is one of the most popular techniques that enables the model to be trained and tested by multiple subsets of data.

8.1.3. Stage 2

Hyperparameters: Hyperparameters can highly influence the robustness of ML models. A list of well-known ML hyperparameters is presented in Table 2 of Ref. [223]. So far, various techniques, including model-free algorithms, gradient-based optimization, Bayesian optimization, multi-fidelity optimization, and MOAs, have been proposed for optimizing hyperparameters, noting that the optimal technique is ML-type dependent [223,240]. While utilizing an optimization algorithm reduces human effort by automating hyperparameter tuning, working with advanced algorithms can be challenging. Many ML models can benefit from simpler methods such as the GS algorithm and manual T&E (A.K.A. babysitting) (Table 1). Moreover, referring to similar earlier studies can supply useful insights to tune a model’s hyperparameters. The sensitivity of the model to a hyperparameter can be monitored through repeatedly computing the accuracy and/or error indicators. For instance, Figure 5 and Figure 6 of Ref. [241] show the variation of accuracy vs. the number of trees for StoGB and variable subsets (and ensemble size) for RotF, respectively. Another example is provided by Ref. [193] (their Figure S5) in which error measurement was used to determine an optimum number of trees for RF, and accuracy measurements were used to determine an optimum tree depth for BRT.

Computational efficiency: The advent of sophisticated methods, such as ensembles and DL, has raised concerns regarding model efficiency [242], especially for complicated environmental simulations such as GHM that demand processing large datasets. Christin, et al. [243] discussed to-be-considered factors (such as programming framework, data provision and augmentation, and required computer power) when applying DL models to ecological studies. Sivakumar, et al. [244] highlighted the following factors to evaluate the efficiency of ML algorithms: (a) training time, (b) prediction time, (c) memory usage, (d) CPU usage, (e) GPU usage, (f) RAM usage, (g) scalability, (h) robustness, and (i) adaptability. They also used an AHP framework to assess the importance of these factors in tackling different problems. The results showed that, depending on the essence of the problem at hand, these factors can be prioritized differently. However, in the absence of powerful computers, training time becomes a critical factor for most DLs and MOA-trained models that require executing deep/or numerous iterations. It is worth mentioning that, depending on the used programming environments, measuring the training and prediction times is readily viable by adding relevant functions (e.g., tic-toc in MATLAB).

Penalty functions can provide valuable insights regarding a model’s complexity. AIC [245] and BIC [246] are among the reputable penalty functions (details in Refs. [247,248]). These metrics can offer two major benefits to ML models, viz. (a) optimizing combinations of predictive variables and (b) performance assessment.

8.1.4. Stage 3

Generalizability and overfitting: In the context of MLGHM, one may ask ’To what extent is the model that is developed for Aquifer A applicable to Aquifer B?’ knowing that the two aquifers may have different characteristics. When these differences are not substantial, area-centric cross-validation can reflect the model’s generalizability. It includes training the model with Aquifer A data and testing it on Aquifer B. However, there are aspects (e.g., bias correction and uncertainty estimation) that require attention [249]. An example of such area-centric cross-validation can be found in Ref. [187], in which Bangladesh data were used to calibrate an LgR model to predict As contamination in South Louisiana, US.

As an impediment to generalizability, overfitting threatens ML models. A general solution to this issue is finding a trade-off between bias (i.e., the error due to oversimplification) and variance (i.e., the model’s sensitivity to small changes in data). Technical details of overfitting and feasible specific solutions are well discussed in relevant studies, such as Refs. [141,250,251,252]. That said, some straightforward methodological hints to deal with overfitting are as follows:

(i)

Possible reasons: Apart from the presence of noise in data and having a limited number of training samples (but with many predictive variables), it is established that the higher a model’s complexity (referred to as high-variance models), the higher the susceptibility to overfitting [250].

(ii)

Indicator: An indicator of overfitting is a considerable difference between the training and testing accuracies (Accuracy_Training >> Accuracy_Testing). Moreover, one may estimate the proneness to overfitting by monitoring accuracy during area-centric and/or data-centric cross-validations.

(iii)

Possible solutions: Feasible solutions to overfitting can include leveraging data augmentation techniques in the event of data insufficiency (as in Ref. [253]); applying feature selection in the case of high dimensionality; using regularization methods (See Table 1); trying simpler (shallower) versions if the current models are too complex (deep); and employing models that are known for being more immune to overfitting (e.g., XGBoost, See Table 1).

Explainability: The growing demand of end-users to replace conventional AI models with explainable ones (noting that Interpretability ⊂ Explainability [254]) may lead to the rejection of opaque-box AI and the switch to XAI. Notwithstanding the growing XAI trends, some argue about the necessity of switching from opaque-box to XAI. As Holm [255] stated, “This blanket rejection of … [opaque-box] methods may be hasty”. A potential reason for such arguments, perhaps, can be sought in the relationship between a model’s explainability and its accuracy, which is usually inverse (see Figure 3 in Ref. [256]; and consideration of DL and DT as examples of opaque-box and XIA models, respectively, of various environmental hazards, e.g., GHM [170], landslide [257], and flood [258]).

This raises an important question: ‘Can we move from opaque-box ML to explainable ML without sacrificing accuracy?’ While attaining a trade-off between accuracy and transparency remains a central consideration, a positive answer to this question may lie in increasing the transparency of accurate models instead of switching to naturally explainable ones, and thereby, maintaining the precedence of modeling accuracy. Some guidelines for increasing the explainability of DL—as one of the most complex ML models—are presented in Text S3 and Figure S7.

Optimization algorithms: Implementing an ML model can be associated with a number of computational challenges, such as local minima, the presence of which may require auxiliary algorithms to achieve a reliable prediction. MOAs can assist ML for proper tuning of the computational variables and model’s hyperparameters to protect the prediction from computational drawbacks. In the surveyed MLGHM literature, several studies were found that optimized ML using MOAs (See Text S4 and Tables S8 and S9).

MOAs cope with computational difficulties through an iterative process. For instance, Figure 4 in Ref. [181] demonstrates the continuous efforts of the applied MOAs; an optimization curve with no degradation in quality, even when no improvement is observed. This either-steady-or-upward trend of the solution’s quality is deemed a significant advantage against conventional ML models that may yield performance decline after several epochs due to overfitting or learning rate issues (e.g., consecutive validation fails, which is a well-known stopping criterion for ANNs). This iterative effort, however, demands time and computational power depending on the algorithm’s nature, which can be partially manifested by the number of required iterations and population size. In most reviewed MOA-based studies, these two factors could have been tuned more carefully as MOAs were executed with a small number of iterations (≤300) and small population sizes (≤100). Owing to the MOAs’ behaviour, some would benefit from larger population sizes and may keep converging even up to 1000 iterations (e.g., in Refs. [259,260]). To address the issue of intensive computations, scientists may also use more efficient MOAs—e.g., electromagnetic field optimization (EFO)—that can perform a high-quality optimization in a reasonable time [237].

8.1.5. Stage 4

Informed hazard zonation:

Hazard zonation can influence exposure results (and subsequently, the ultimate risk assessment), leading to substantial health and/or monetary impacts on the stakeholders (e.g., people, government, and NGOs). Therefore, as one of the final steps of GHM, utilizing a proper classification strategy is of utmost importance. There are several classification methods of modeled environmental hazards. Natural Breaks (Jenks’ optimization method [261]), Equal Intervals, and Quantiles are among the widely used methods, each with specific pros and cons. More recently, models leverage the receiver operating characteristic (ROC) curve to find a cutoff point that optimally differentiates hazard levels. For instance, Cantarino, et al. [262] proposed a new ROC-based model for landslide susceptibility mapping. They reported a considerable distinction (>20% of the surface) between different models in detecting the most susceptible parts. As for GHM, Wu and Polya [263] proposed a potentially cost-saving ROC-based objective cost-benefit informed criteria, which led to different cutoff values for identifying high and low groundwater arsenic hazard.

8.2. Future Directions

This section addresses some emerging directions that can hold promise to attain advanced MLGHM in future efforts.

(i)

Although XAI was discussed earlier (e.g., Section 8.1.4), increasing the transparency is still considered a significant emerging direction towards enhancing stakeholders’ trust in modeling outcomes. This study offered an example of moving from opaque-box to transparent-box for DL (see Text S3 and Figure S7). However, other methods, such as SHAP, along with monotonic constraints [264], can be helpful to elucidate models’ calculations.

(ii)

Employing PIML models—embedding physical laws into learning algorithms—is another growing frontier to enhance scientific plausibility and reliability of the model under extrapolation [265,266]. An example of this in MLGHM works can be incorporating hydrogeological rules (e.g., groundwater flow directs contamination, hence, no upgradient contamination movement) into the mathematical computations of the predictive model.

(iii)

The use of IoT-empowered sensing networks can enrich modeling by providing continuous, real-time data [267,268]. It can also lead to more realistic results due to analyzing dynamic conditions of the predicted and predictive factors instead of static data.

(iv)

Transfer learning (e.g., fine-tuning a pre-trained model with limited data from the new to-be-assessed region) [269] and federated learning (e.g., collaborative training of models without sharing raw data) [270] are two approaches that can contribute to tackling challenges stemming from data scarcity and data privacy.

(v)

While many traditional hazard zonation models are easily accessible in software such as GIS, more recent models may require external tools (and more statistical knowledge) to implement, making them challenging to use for some. Hence, future efforts should also focus on developing user-friendly graphical user interfaces (GUIs) to facilitate the use of GHM models and new hazard classification methods.

These directions, together with concepts discussed in Section 5, Section 6, Section 7 and Section 8, suggest that the basis for strengthening the role of next-generation ML in GHM (and generally sustainable water resource management) will go beyond technical accuracy alone, extending to the model’s real-time applicability and scientific consistency.

9. Conclusions

The main conclusions of this systematic survey of 284 ML in groundwater hazard mapping (MLGHM) articles published over the period 2005–2024 are summarized below.

(i)

There has been an exponential increase in published applications of MLGHM models over the past two decades.

(ii)

Iran, India, the US, and China are the countries most modeled in these studies, but there are many other countries that would benefit from (further) MLGHM.

(iii)

Nitrate, water quality index, and arsenic featured as the most studied target groundwater quality indicators. The most frequently considered categories of predictive variables were groundwater chemical characteristics and geomorphological factors.

(iv)

Tree-based ML was the most popular feature selection method.

(v)

Tree-based ML (mostly RF) was the most popular MLGHM model.

(vi)

Published evaluations of model superiority have been largely based on accuracy. On the basis of many articles, resampling-improved ensembles, meta-model ensembles, and tree-based models outperformed a wide variety of models, including (but not limited to) shallow ANNs, SVMs, NFs, and regression models. A more detailed accuracy comparison (based on the existing pieces of evidence) then reflected a close competition among boosting ensembles, random forest, and deep learning as the most promising members of their families.

(vii)

Aside from accuracy, other key factors—notably including model complexity and predictability—have been largely overlooked in assessing ML model quality, notwithstanding their often key importance in determining what are better models for particular types of problems.

(viii)

We present a flowchart that can inform GHM researchers to help better select the most appropriate popular ML models on the basis of requirements for (a) accuracy, (b) transparency, (c) training speed, and (d) number of hyperparameters, as well as (e) the intended modeling scale and (f) required user’s expertise.

(ix)

Notable gaps that were identified in the surveyed studies were discussed in depth, and several ideas were suggested for optimizing MLGHM models by emphasizing the features of a ‘better model’.

Whilst this review has covered a large number of high-quality articles, some articles might have been missed by the search strings or due to the rapid developments in the field of MLGHM. Challenges in both classifying reported variables and models are acknowledged due, in part, to differences in terminology reported. Robust global conclusions were precluded for some model types because of a paucity of studies or reported model quality criteria (other than accuracy) in many other studies.