A Systematic Literature Review of MODFLOW Combined with Artificial Neural Networks (ANNs) for Groundwater Flow Modelling

Abstract

The sustainable management of global groundwater resources is increasingly challenged by climatic uncertainty and escalating anthropogenic stress. Thus, there is a need for simulation tools that are more robust and flexible. This systematic review addresses the integration of two dominant modeling paradigms: the physically grounded Modular Finite-Difference Flow (MODFLOW) model and the data-agile Artificial Neural Network (ANN). While the MODFLOW model provides deep process-based understanding, it is often limited by extensive data requirements and computational intensity. In contrast, an ANN offers remarkable predictive accuracy and computational efficiency, particularly in complex, non-linear systems, but traditionally lacks physical interpretability. This review synthesizes existing research to present a functional classification framework for MODFLOW–ANN integration, providing a systematic analysis of the literature within this structure. Our analysis of the literature, sourced from Scopus, Web of Science, and Google Scholar reveals a clear trend of the strategic integration of these models, representing a new trend in hydrogeological simulation. The literature reveals a classification framework that categorizes the primary integration strategies into three distinct approaches: (1) training an ANN on MODFLOW model outputs to create computationally efficient surrogate models; (2) using an ANN to estimate physical parameters for improved MODFLOW model calibration; and (3) applying ANNs as post-processors to correct systematic errors in MODFLOW model simulations. Our analysis reveals that these hybrid methods consistently outperform standalone approaches by leveraging ANNs for computational acceleration through surrogate modeling, for enhanced model calibration via intelligent parameter estimation, and for improved accuracy through systematic error correction.

1. Introduction

Groundwater modeling is essential for the management of present-day water resources. It provides an essential tool for protecting water quality, forecasting aquifer dynamics, and understanding complex subsurface hydrological systems. The field of groundwater modeling has evolved significantly over time, progressing from early empirical methods to the sophisticated computational tools available today. Early civilizations, such as the Romans and Persians, engineered advanced water management systems like aqueducts and qanats. The design and placement of these structures were based on empirical observations of local geology and hydrological conditions [1]. The scientific formalization of groundwater hydrology began in the 19th century with Henry Darcy’s foundational work on water movement through porous media [2]. This foundation was expanded upon by pioneers such as Jules Dupuit and Philip Forchheimer, who developed fundamental theories of well hydraulics and aquifer behavior [3,4]. A major advancement came in 1935 with the Theis equation, which provided the first analytical method for modeling transient (time-varying) groundwater flow [5].

The advancement of digital computing in the latter half of the 20th century caused a fundamental shift in groundwater modeling, enabling the numerical solution of the complex partial differential equations that govern groundwater flow [6]. This computational shift led the development of advanced, physics-based simulation models [7]. Most important among them was the U.S. Geological Survey’s MODFLOW model, first released in 1984, which has since then emerged as a global standard for groundwater modeling [8,9]. The primary strengths of the MODFLOW model are its modular structure and its foundation in physical principles, enabling it to simulate a wide variety of aquifer systems and hydrological conditions [10,11]. Despite its physical basis, the model has notable limitations. It demands large datasets for calibration, is often computationally expensive, and requires a time-consuming iterative process to match simulation results to field observations [12].

In parallel, data-driven methods, particularly Artificial Neural Networks (ANNs), have emerged as a powerful alternative to physics-based modeling. ANNs operate on a fundamentally different principle. Instead of being programmed with explicit physical laws, they learn complex, non-linear relationships directly from historical data [13,14]. This approach makes them highly effective for predictive tasks, especially in geologically complex settings, such as karstic or hard-rock aquifers, where the underlying physical processes are difficult to fully parameterize. However, the primary limitation of such data-driven models is their lack of direct physical interpretability, i.e., the black box problem. This is a critical drawback in decision-making scenarios that require not only an accurate prediction but also a clear understanding of its underlying physical basis [15].

The most widely accepted research in this field today focuses on combining these two powerful but fundamentally different approaches. Hybrid models create a powerful synergy by leveraging the complementary strengths of numerical and machine learning methods [16]. The MODFLOW model grounds the system in physical reality, ensuring adherence to hydrological laws, while ANNs provide exceptional computational speed and the ability to identify complex non-linearities in the data. This integration of physical principles with data-driven pattern recognition unlocks a modeling capability that is more rapid, robust, and accurate than either paradigm used alone. While narrative reviews of MODFLOW models or ANNs exist, and some studies offer direct comparisons, a comprehensive systematic review that categorizes the functional classification of the integration strategies that constitute MODFLOW–ANN integration has been missing in the literature [17,18]. This review addresses this gap by presenting a functional classification framework for MODFLOW–ANN integration and synthesizes the literature within this structure. The primary objectives of this paper are: (1) To systematically identify and synthesize the literature on MODFLOW-ANN integration for groundwater flow modeling published between 2003 and 2005, using a documented and replicable search strategy. (2) To present a classification of integration strategies, such as surrogate modeling, parameter estimation, and error correction. (3) To analyze the applications, reported advantages, and persistent limitations within this classification framework, thereby identifying key trends and future research directions.

2. Systematic Review Methodology

We followed a clear plan to conduct this literature review. Our approach included setting specific research questions, using a well-documented search strategy, applying clear rules for selecting studies, and having a consistent process for gathering and combining data [19,20].

2.1. Research Questions

We used three specific research questions (RQs) to focus our review on our search, data collection, and analysis. These questions were created to meet the study’s main goals: to map out when and where MODFLOW models and ANNs have been used together, to group the different ways they are combined, and to assess the results of each method.

• RQ1: What is the temporal and geographical distribution of research integrating MODFLOW models and ANNs for groundwater flow modeling?
• RQ2: What are the primary strategies for integrating MODFLOW models and ANNs, and what is their relative prevalence in the literature?
• RQ3: What are the reported advantages, limitations, and performance outcomes for each integration strategy?

2.2. Finding and Identifying Studies

We carried out a thorough and methodical search of published research to find all relevant studies. The search covered a 20-year period from 1 January 2003 to 3 March 2025. We chose this timeframe to track how these combined modeling techniques have grown from their early days to their recent increase in use [21].

We searched three major online databases: Scopus, Web of Science, and Google Scholar. We selected these sources because they offer broad and overlapping coverage of research in water science, environmental studies, and computer engineering. This helped us make sure that we found as many relevant publications as possible.

Our search terms were developed carefully through a process of trial and error. This was to get a good balance between finding all relevant studies and filtering out irrelevant ones [20]. To make our search process clear and repeatable, the exact search terms we used are listed in

Table 1. Database Search Strategy.

Database	Search String
Scopus	TITLE-ABS-KEY(MODFLOW AND (“Artificial Neural Network” OR ANN) AND (groundwater OR aquifer)) AND (PUBYEAR > 2002 AND PUBYEAR < 2025)
Web of Science	TS = (MODFLOW AND (“Artificial Neural Network” OR ANN) AND (groundwater OR aquifer OR “ground water”)) AND PY = (2003–2025)
Google Scholar	MODFLOW “Artificial Neural Network” OR ANN OR “hybrid model” OR “coupled model” groundwater

. A consistent and well-defined search plan is vital for a good systematic review. It ensures that the initial set of articles is collected in a fair and repeatable way. Using inconsistent dates or search terms would have made our findings less reliable.

2.3. Study Selection Criteria

To ensure the objectivity and consistency of the review, a formal set of inclusion and exclusion criteria was established prior to the screening process. A two-stage screening process was then conducted by two authors independently to minimize bias, with any disagreements resolved through consensus discussion. The first stage involved screening the titles and abstracts of all retrieved records. The second stage involved a full-text review of the articles that passed the initial screen [22]. The criteria are outlined in

Table 2. Inclusion and exclusion criteria.

Inclusion Criteria	Exclusion Criteria
Peer-reviewed journal articles or full conference reports.	Non-peer-reviewed publications, such as editorials, conference papers, abstracts, notes, case reports, and short commentaries.
Publications written exclusively in English, between 1 January 2003 and 30 March 2025.	Studies that only focus on surface water
Studies explicitly investigating groundwater flow modeling, MODFLOW models, ANNs, and hybrid models.	Studies only relevant to solute movement or water quality, without a clear connection to groundwater flow modelling.

.

2.4. Data Extraction and Synthesis

For each study that met the final inclusion criteria, a standardized data extraction form was used to systematically collect relevant information. This process was designed to directly address the research questions and included capturing of the following details: author and year of publication, study location/country, primary scientific objective, the specific integration strategy employed, key findings and conclusions, and any reported performance metrics (e.g., Coefficient of Determination (R²), Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency (NSE)). The extracted data were then thematically synthesized to identify patterns, trends, and overarching conclusions, which form the analytical basis of the subsequent sections of this review.

3. The Physical-Based Model: MODFLOW

For four decades, the Modular Finite-Difference Flow (MODFLOW) model has been the cornerstone of quantitative groundwater investigation globally. Because it is dependable, flexible, and well-documented, this open source code distributed by the U.S. Geological Survey is now the go-to tool for modeling groundwater flow in both professional and academic settings [23]. MODFLOW is a widely used groundwater modeling software that numerically solves the three-dimensional, transient groundwater flow equation using a finite-difference approach [24]. The flow is governed by the Boussinesq Equation, which is a combination of Darcy’s Law and the principle of mass conservation [9].

$${\displaystyle \frac{\partial }{\partial x}}\left(K_{xx}{\displaystyle \frac{\partial h}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(K_{yy}{\displaystyle \frac{\partial h}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(K_{zz}{\displaystyle \frac{\partial h}{\partial z}}\right)-W=Ss{\displaystyle \frac{\partial h}{\partial T}}$$

(1)

where, $K_{xx}$, $K_{yy}$, and $K_{zz}$ are the values of hydraulic conductivity on the x, y, and z axes. W is volumetric flux per unit volume representing the source and sinks of water [t⁻¹]. S_s is the specific storage of the permeable material [L⁻¹], h the is potentiometric head [L], and T is time.

The widespread adoption and success of MODFLOW is due to its fundamental modular structure. The software is built around a series of independent modules, known as “Packages”. Each package is designed to simulate a specific hydrological process or feature, such as wells (WEL), recharge (RCH), or rivers (RIV) [11,25]. This design not only provides the flexibility to perform simulations to specific hydrogeological problems but also facilitates the integration of MODFLOW with other computational frameworks such as ANNs [26].

MODFLOW is continuously evolving, with key versions like MODFLOW-2005 and MODFLOW 6 (2017) offering modern, object-oriented frameworks. As summarized in

Table 3. Advancement in MODFLOW through time.

Year	Advancement/Development	Significance	Ref.
1984	Initial release of MODFLOW by the USGS	Revolutionized groundwater modeling by providing a modular, finite-difference approach for simulating groundwater flow.	[9]
1990	Development of Visual MODFLOW	Simplified the modeling process with a user-friendly graphical interface, making MODFLOW accessible to a broader audience.	[25]
2000	Integration with MT3DMS for solute transport modeling	Enabled combined groundwater flow and contaminant transport simulations critical for water quality management.	[27]
2010	Coupling with GIS and remote-sensing tools	Enhanced model inputs and calibration using spatial datasets, improving the accuracy of hydrological assessments.	[26]
2012	Development of MODFLOW-USG (Unstructured Grid)	Allowed for irregular grids, enabling more precise representation of complex hydrogeological features.	[28]
2015	Integration with SWAT and other surface water models	Facilitated comprehensive watershed-scale hydrological simulations, linking groundwater and surface water dynamics.	[29]
2020	High-performance computing (HPC) and ML integration	Improved the efficiency of large-scale and real-time simulations while enhancing predictions in data-scarce regions through ML.	[30]

, this evolution is driven by the growing complexity of hydrogeological challenges and the corresponding demand for more integrated modeling solutions.

MODFLOW Applications in Groundwater Modelling

MODFLOW has proven to be a highly versatile tool, successfully used to address scientific problems across a wide spectrum of hydrogeological conditions. Globally, researchers have employed the model to simulate complex phenomena such as surface-subsurface interactions, solute transport, and groundwater flow dynamics. The diverse applications of the MODFLOW model demonstrate its utility. For instance, studies have used the model to assess the performance of multi-aquifer wells [26], simulate the unique hydrology of peatlands [31], and support critical infrastructure planning [32].

Furthermore, the MODFLOW model’s capabilities are frequently expanded by coupling it with other specialized models to create more comprehensive simulations. A key example is its integration with the Soil and Water Assessment Tool (SWAT), which improves low-flow simulations in river basins by linking watershed-scale surface processes with subsurface flow [33]. In a similar manner, coupling the MODFLOW model with agent-based land-use models allows researchers to evaluate the long-term impacts of different zoning policies on groundwater resources, offering a powerful tool for sustainable planning [34,35].

The model has been particularly critical in nations like India, which confront acute water stress and significant hydrogeological diversity. MODFLOW has been instrumental in quantifying and managing groundwater depletion, a critical issue within India’s agricultural heartlands. For example, long-term simulations in central Punjab documented significant annual water table declines of 0.15–0.20 m over a 30-year period, providing clear, quantitative evidence of unsustainable groundwater extraction rates [36]. Two studies showed that the MODFLOW model was successful in simulating recharge-driven water table fluctuations in the Sonar sub-basin. One demonstrated the dominance of recharge over pumping in influencing water table changes, while the other created a two-layer aquifer model using observed and pumping well data to simulate dynamic responses under various stress conditions [37,38]. In southern India, such as in the Tirunelveli district of Tamil Nadu, GIS-based MODFLOW models have been used to assess over-extraction risks and delineate areas vulnerable to depletion, thereby informing more targeted and sustainable water management strategies [39]. MODFLOW and its associated transport models, like MT3DMS and SEAWAT, are vital for tackling a wide range of water quality. Along extensive coastlines, these models are critical for simulating and preventing seawater intrusion. Studies in the coastal aquifers of Balasore (Odisha) and Gujarat in India have used MODFLOW to evaluate different pumping scenarios and recommend sustainable extraction caps to mitigate salinity risk [40]. In industrial and agricultural hubs, such as Tamil Nadu’s Amaravathi River basin, MODFLOW simulations have been used to track the transport of contaminants like total dissolved solids (TDS) from industrial effluents, providing a scientific basis for pollution control measures [41].

Recognizing that groundwater and surface water are interconnected, many studies have focused on integrated modeling. Research in the Mahesh River basin demonstrated the enhanced predictive capacity of coupled surface–groundwater models, which more accurately captured the aquifer’s response to hydrological stresses [42]. Similarly, work in the Mahanadi delta has successfully captured the dynamic river–aquifer interactions that govern the region’s hydrology [43].

To provide a consolidated overview,

Table 4. Summary of the literature on groundwater modelling using MODFLOW.

Ref.	Study Area	Model(s) Used	Key Input Data	Findings
[39]	Tirunelveli, Tamil Nadu	MODFLOW	Geology, soil, hydraulic heads, daily rainfall, well yield	The negative water budget in the study area indicates over-extraction and the need for better management.
[40]	Balasore, Orissa	Visual MODFLOW	Salinity, hydraulic conductivity, specific storage, recharge, river influence	The strategy advises reducing downstream pumping and increasing it at specific sites for sustainability.
[41]	Amaravathi River Basin, Tamil Nadu	Visual MODFLOW	Effluent discharge with TDS, lithology, hydrogeological parameters	Effluent from dyeing units severely harms groundwater quality; stopping discharge improves it over 15 years.
[42]	Mahesh River Basin, Maharashtra	MODFLOW	Hydrological, hydrogeological, rainfall, well data	Coupling surface and groundwater models improves accuracy and prediction of aquifer behavior.
[44]	Western United States	MODFLOW	Hydraulic heads, well radius, transmissivity, boundary heads	The MAW1 Package aligns well with analytical solutions and is not sensitive to grid refinement.
[45]	-	SEAWAT, MODFLOW, MT3DMS	Boundary conditions, initial fluid distribution	For the 3D saltpool problem, SEAWAT results were reasonable but had some discrepancies.
[46]	Musimcheon Basin, South Korea	MODFLOW	Land use, surface runoff, hydraulic conductivity, specific yield, recharge	The integrated SWAT-MODFLOW model improved simulation of drawdown and reduced streamflow from pumping.
[47]	-	MODFLOW, HydroGeoSphere (HGS)	Hydraulic conductivity, river geometry, van Genuchten parameters	Neglecting the unsaturated zone in MODFLOW underestimates infiltration flux, especially for disconnected systems.
[48]	Monroe County, Michigan	MODFLOW-2000	GIS spatial data: road infrastructure, soil quality, distances	The model links groundwater flow and decision-making, highlighting policy impacts on water resources.
[49]	Canada	MODFLOW	Hydrogeological properties, boundary conditions, stresses (wells, recharge)	Multiple model layers enhance accuracy for complex sites. Diverse evidence for calibration is crucial.
[50]	-	MODFLOW	Conductivity, specific yield/storage, prescribed heads, recharge rates	A stable method uses upstream weighting, Newton–Raphson linearization, and an ORTHOMIN solver.
[51]	Iran	MODFLOW, MT3DMS	Topographical and bedrock surface, initial head conditions	Groundwater levels will drop by 15 m in 10 years. Rising chloride and EC levels threaten water quality.
[52]	Sloping aquifer	MODFLOW-SP	Aquifer geometry, specific yield, hydraulic conductivity, river levels	MODFLOW-SP accurately predicts hydraulic heads in unconfined aquifers with slopes under 26.6 degrees.
[53]	-	MODFLOW, Harmony Search Algorithm	Pumping well positions, total water demand	Coupling flow simulation with optimization models streamlines complex groundwater management.
[54]	Oman	MODFLOW	Borehole data, rainfall, initial hydraulic conductivity	Manual calibration with PEST is advised for complex geology.
[55]	Texas, USA	SWAT+, MODFLOW	Land use, soil, DEM, hydraulic properties, groundwater balance	SWAT+ effectively models groundwater flow and interactions, improving hydrological simulation accuracy.
[56]	Poland	MODFLOW	Filtration coefficient, layer drainage, conductivity of channel zone	Using 100 cm high dams in forest areas can boost water retention by 38% compared to no dams.
[57]	Lower Palar River Basin, Tamil Nadu	MODFLOW	Hydraulic conductivity, abstraction rates, recharge rates	Pumping an extra 2 MGD would cause the groundwater head to drop below sea level in the eastern area.
[58]	Vaishali Canal, Bihar	MODFLOW	Remote sensing data (IRS-1A/1C LISS sensors)	Integrating remote sensing and GIS with flow modeling helps identify waterlogged areas.
[59]	Punjab	Visual MODFLOW	Rainfall, evaporation, soil characteristics, agricultural data	The model highlighted the impact of the Wheat-Paddy cropping pattern on groundwater recharge and depletion.
[60]	Sonar Sub-basin, Madhya Pradesh	Visual MODFLOW	Hydraulic conductivity, storage coefficient, water levels, recharge rates	Groundwater levels were accurately simulated, with minimal impact from pumping rates.
[61]	Osmansagar and Himayathsagar, Telangana	Visual MODFLOW	Recharge, groundwater draft, withdrawal rates	Continuing current withdrawal rates could lower water levels by over 45 m by 2020.
[62]	Jammu and Kashmir	MODFLOW	Hydro-geomorphological features, borewell data, seepage estimates	Perforated pipes in the tunnel effectively drained groundwater seepage, matching observed rates.
[63]	Kadalundi River Basin, Kerala	Visual MODFLOW	Base map, calibration/validation data, pumping data	The basin may remain safe for five years, but the water table will eventually reach bedrock, requiring artificial recharge.
[64]	Mahanadi Delta, Odisha	Visual MODFLOW, PEST	Hydraulic head data, conductivities, specific yield, annual outflow	The model showed groundwater depletion from agriculture and net outflow into the Bay of Bengal.
[65]	Una Coastal Region, Gujarat	MODFLOW, SWI2	Water samples, seawater infiltration, transmissivity data	Pumping increases seawater intrusion but reducing pumping rates can mitigate this.

summarizes key studies utilizing MODFLOW worldwide, with an emphasis on Indian context, highlighting the diverse challenges addressed by this versatile model.

4. Artificial Neural Networks (ANNs)

The field of machine learning (ML) has guided in a new era for groundwater flow modeling, significantly enhancing computational efficiency, predictive accuracy, and robustness [66]. Among the various ML techniques, Artificial Neural Networks (ANNs) have gained prominence for their ability to handle the complex, nonlinear relationships inherent in hydrological systems. ANNs excel at processing large datasets, identifying hidden patterns, and adapting to the non-stationary characteristics of groundwater dynamics, making them a powerful complement to traditional physics-based models [67,68].

An ANN is a computational system inspired by the structure and function of biological neural networks. It is composed of interconnected nodes, or “neurons,” arranged in layers: an input layer, one or more hidden layers, and an output layer [69]. The network learns by adjusting the numerical weights of the connections between neurons during a training process, effectively teaching itself to map a set of inputs (e.g., rainfall, pumping rates) to a desired output (e.g., groundwater level) without being explicitly programmed with governing physical equations [70].

While conventional ANNs provide highly accurate approximations, a persistent criticism has been their potential lack of physical consistency i.e., the black box model [71]. To address this, a new class of models known as physics-informed neural networks (PINNs) have emerged. PINNs represent a significant advancement by incorporating the governing physical equations, such as the groundwater flow equation, directly into the ANN’s training process. This is achieved by adding a loss function that measures how much the network’s output conflicts with known physical laws. The model is then trained to minimize this conflict, resulting in a solution that agrees with both the training data and the fundamental principles of physics [72,73,74].

Overall, these studies highlight the adaptability of ANNs in a wide range of hydrological contexts. ANNs have consistently demonstrated strong performance in predicting groundwater levels, quality, and flow. This effectiveness is maintained across various applications, whether they are used as standalone models, in hybrid systems, or integrated with GIS and optimization algorithms.

As illustrated in Figure 1, the annual publication trend on this topic shows a significant increase in research activity after 2020. This recent surge is likely driven by a convergence of technological advancements and pressing environmental challenges. The increased accessibility of high-performance computing and powerful open-source machine learning libraries has provided the necessary tools, while the urgent need to understand climate change’s impact on groundwater provides critical motivation.

• We identified about 250 key terms by looking at the most frequently occurring words (at least ten times) in the titles and abstracts of research papers pertaining to groundwater. These terms were divided into four primary groups, each of which stood for a significant field of study in Figure 2.
• Many terms were included in the first cluster (dark purple), which focused on subjects pertaining to ML applications, specifically the use of artificial neural networks for environmental prediction. Artificial, neural, network, model, machine, support vector, learning, prediction, ANN, and forecasting were among the most prominent terms in this cluster.
• The second cluster (green–blue) concentrated on hydrological processes and the evaluation of groundwater quantity and quality. Groundwater, aquifer, level, fluctuation, depth, recharge, soil, quality, transport, and contamination were among the terms it included.
• Terms related to time-series analysis and forecasting, frequently in combination with neural networks, made up the third cluster (yellow). Forecasting, wavelet, trends, time series, uncertainty, performance, and optimization were among the terms that appeared frequently.

Application of ANNs in Groundwater Flow Simulation

Standalone ANN models have been successfully applied to a wide range of groundwater problems across diverse hydrogeological and geographic contexts globally. They have been used to forecast the spatial distribution of nitrate contamination from agricultural sources [75], predict groundwater level fluctuations in advance [76], and forecast tidally influenced groundwater dynamics along coastal aquifers [77]. In geologically complex systems, such as karstic or fractured rock aquifers, where the assumptions of traditional numerical models may not hold, ANNs have proven to be particularly effective [78]. Hybrid models that combine ANNs with other data-driven techniques, such as wavelet decomposition for time-series pre-processing, have demonstrated even greater accuracy [79,80]. These studies collectively highlight the remarkable adaptability and predictive power of ANNs in a wide range of hydrological settings, consistently demonstrating strong performance in forecasting groundwater levels, quality, and flow dynamics.

In India, ANNs have become a widely adopted tool for modeling groundwater dynamics and forecasting future scenarios, particularly in regions with limited hydrogeological data. Early applications focused on solving complex inverse problems, such as identifying unknown sources of pollution by learning the relationship between observed contaminant concentrations and their potential fluxes [81]. More recent studies have demonstrated increasing sophistication. For instance, researchers have coupled ANNs with Genetic Algorithms to simulate flow and contaminant transport under conditions of uncertainty [82], and have applied feedforward ANNs in the complex hard rock terrains of southern India to inform sustainable management strategies [83]. A significant trend has been the coupling of ANNs with MODFLOW models to optimize agricultural water use, a critical issue for India’s food security. In these applications, ANNs are used to develop optimal cropping patterns that maximize yield while minimizing groundwater depletion, with MODFLOW providing the underlying simulation of the aquifer’s response. These studies collectively highlight the remarkable adaptability and predictive power of ANNs in a wide range of hydrological settings. They consistently demonstrate strong performance in forecasting groundwater levels, quality, and flow dynamics.

Table 5. Summary of the literature on groundwater modelling using ANNs.

Ref.	Study Area	Model(s) Used	Key Input Data	Findings
[84]	-	ANN	Soil water, nitrate concentration, discharge rate, fertilizer concentration	ANN model with a 6-10-6-1 architecture accurately estimated soil nitrate distribution (R2 = 0.83).
[85]	Messara, Greece	ANN (Levenberg–Marquardt)	Rainfall, temperature, well depth, groundwater level	Standard FNN accurately predicts groundwater levels up to 18 months in advance.
[86]	Brindisi, Italy	MO-IODNN	Rainfall, groundwater level time series	NARX suits long-term predictions, while ARX is ideal for short-term forecasts.
[87]	Australia	ANN, MATLAB	Water table, hydraulic conductivity, tide elevation, beach slope	ANN model successfully predicted groundwater fluctuations and tide variations accurately within 100 m from the coastline.
[88]	-	ANN	Transmissivity, hydraulic conductivity, constant head values, well extraction	The hybrid approach of combining ANNs with numerical models reduces predictive errors.
[89]	Tabriz, Azerbaijan	ANN (LM algorithm)	Temperature, rainfall, mean discharge, groundwater level	The Spatio-Temporal ANN (STANN) model shows higher efficiency compared to other hybrid models.
[90]	Samcheok, South Korea	MATLAB	DEM, slope gradient, groundwater level, permeability, geology, land use	The ANN model achieved 96.06% accuracy in predicting ground subsidence.
[91]	Kerman Plain, Iran	ANN, ANFIS	Monthly groundwater levels, air temperature, rainfall	Neuro-fuzzy methods show superior performance for groundwater level prediction.
[92]	Qorveh Plain, Iran	WANN, MLP, FF-ANN	Groundwater level data from 26 piezometers	The WANN model, using db2 and db4 wavelets, outperformed other wavelets in forecasting.
[93]	Karaj Plain, Iran	ANFIS, GP (MATLAB)	Groundwater level, precipitation, evaporation	Genetic Programming (GP) outperforms ANFIS, especially when using combined surface and groundwater data.
[94]	Turkey	ANFIS, RBNN, SVM	Monthly groundwater level, precipitation, average temperature	SVM-RBF and SVM-PK models showed the highest accuracy in predicting groundwater levels.
[95]	Arak Plain, Iran	ANN (Neurosolution)	Transmissivity, altitude, precipitation, evaporation, groundwater level	The ANN model surpassed the MLR method in predicting groundwater depth, demonstrating superior accuracy.
[96]	Aspas Aquifer, Iran	ANN, SVR, WT, CEEMD	Precipitation, temperature, evaporation, groundwater level	The CEEMD–ANN hybrid model outperformed other models and the GRACE satellite algorithm in prediction.
[97]	-	ANN	Rainfall, temperature, relative humidity	The ANN approach effectively estimates unknown groundwater pollution sources.
[98]	Vamsadhara River Basin	FF-BP ANN	Rainfall, runoff, suspended sediment yield	Generalized pattern-learned models demonstrated superior performance overall.
[99]	Godavari Delta, Andhra Pradesh	ANN	Rainfall, canal release	The ANN models proved statistically adequate, accurately predicting water levels.
[100]	-	ANN	Rainfall, recharge, transmissivity, pumping rate	The ANN approach measured uncertainty in simulations efficiently, reducing computational effort.
[101]	Maheshwaram Watershed, Telangana	FFNN, LMB	Rainfall, temperature, evaporation, relative humidity	The FFNN-LMB model demonstrated high accuracy (93%) in forecasting monthly groundwater level fluctuations.
[102]	Orissa	ANN (BR algorithm)	Weekly rainfall, evaporation, river stage, water level	The ANN accurately predicted groundwater levels one week ahead at 18 sites.
[103]	Kavaratti Islands, Lakshadweep	ANN	Rainfall, topology, runoff	The ANN model recommended pumping rates below 13,000 L/day to stabilize salinity.
[104]	Ranga Reddy, Telangana	FFNN-LM, ANFIS	Rainfall, temperatures, evaporation, relative humidity	Both models provided high accuracy for forecasting groundwater levels (R2 > 0.93).
[105]	Chennai	MLR, PCR, ANN, PC-ANN	Temperature, EC, pH, TDS, nitrate, sodium, chloride	The PC-ANN model outperformed all others in predicting nitrite concentration.
[106]	Udupi	PSO, ANN model	Groundwater level, rainfall data	The hybrid ANN-PSO algorithm predicts groundwater levels more accurately than the standard backpropagation algorithm.
[107]	New Delhi	ANN, Random Forest, ARIMA	Groundwater level, temperature, rainfall, humidity	The ANN model outperformed SVM and LR in predicting groundwater levels.
[108]	Delhi	ANN	Groundwater level, rainfall, population, temperature	The 3-15-1 ANN model architecture is the most effective for predicting groundwater fluctuations in urban areas.
[109]	Punjab	MLP, LSTM, SARIMA	Rainfall, groundwater level	Both MLP and LSTM models outperformed SARIMA, with MLP slightly better for pre-monsoon and LSTM excelling post-monsoon.
[110]	Pravara River Basin	ANN, ANFIS	Annual temperature, rainfall, groundwater level	The ANFIS model outperformed the ANN model in predicting groundwater levels (R2 of 0.817 vs. 0.763).

summarizes the use of ANNs in groundwater studies, illustrating the increasing importance and versatility of these models.

5. A Classification Framework of MODFLOW–ANN Integration

The integration of MODFLOW models and ANNs is not a single approach but a collection of distinct strategies, each designed to leverage the complementary strengths of both models. Our systematic review of the literature revealed three primary integration strategies that form a classification framework for understanding the hybrid groundwater modeling, as shown in Figure 3.

This framework depicts the integration of MODFLOW models with ANNs through three interconnected pathways: parameter estimation, surrogate modeling, and error correction. In Pathway 1, field observations such as hydraulic head and geological data are used to train an ANN model for estimating hydrogeological parameters, which are then incorporated into MODFLOW. In Pathway 2, MODFLOW outputs are used to train ANN-based surrogate models that replicate their behavior for faster simulations; and in Pathway 3, residuals between MODFLOW predictions and observed data are used to train a secondary ANN that corrects the model outputs. To substantiate the utility of this functional framework,

Table 6. Comparative analysis of hydrogeological and machine learning classification frameworks.

Framework Type	Classification Basis	Key Categories	Primary Utility	Ref.
Functional Framework	The functional role of the ANN within the physical modeling workflow.	(1) Surrogate Modeling (emulation), (2) Parameter Estimation (input improvement), (3) Error Correction (output refinement)	Provides a practical guide for hydrogeologists on how and why to integrate an ANN with MODFLOW to solve specific modeling challenges.	[111,112]
Algorithmic ML Framework	The type of machine learning algorithm and its learning style.	Supervised (e.g., ANN, SVM), unsupervised (e.g., Clustering, SOM), ensemble (e.g., Random Forest)	Catalogues the spectrum of ML techniques applied in a domain. Useful for data scientists selecting appropriate algorithms based on data structure and task.	[113]
Multiscale Modeling Framework (e.g., MAP)	The degree of spatial, temporal, and physical processes coupling between models at different scales.	Hierarchical vs. concurrent top-down vs. bottom-up loose vs. tight coupling	A platform for selecting appropriate multiscale simulation methods for complex systems where processes occur at disparate scales.	[114]

provides a comparative analysis against other classification schemes found in the literature. This comparison highlights how this functional framework, synthesized from the literature, offers a practical perspective for hydrogeologists that is distinct from frameworks based on algorithm type or modeling scale.

Together, these pathways form a hybrid modeling approach that strengthens the predictive reliability and computational efficiency of groundwater flow simulations.

Table 7. A classification framework of MODFLOW–ANN integration strategies.

Integration Strategy	Core Objective	Role of MODFLOW	Role of ANN	Key Advantage	Ref.
Surrogate Modeling	Accelerate computation	Generates training data (input–output pairs)	Learns the input–output mapping to emulate MODFLOW	Computational efficiency for optimization/uncertainty analysis	[115,116,117]
Parameter Estimation	Improve model inputs and calibration	Simulates flow based on ANN-estimated parameters	Learns the inverse relationship (e.g., heads to conductivity)	Automates and improves estimation of heterogeneous parameters	[118]
Error Correction	Refine model predictions	Provides the primary physics-based prediction	Models the systematic error (residuals) of the MODFLOW prediction	Corrects for unmodeled physics and conceptual errors	[119,120]

provides a concise overview of this analytical framework.

5.1. Strategy 1: An ANN as a Surrogate Model

In this strategy, a computationally expensive MODFLOW model is run numerous times to generate a large dataset of inputs and corresponding outputs. An ANN is then trained on this dataset to act as a fast and accurate emulator, or “surrogate”, of the physical model [121]. The primary motivation is computational efficiency, which is crucial for applications requiring thousands of model runs, such as uncertainty analysis via Monte Carlo simulations or simulation–optimization for resource management [122]. A recent example is the ‘Dual Path CNN-MLP’ model developed for the Qatar aquifer, which served as a surrogate for MODFLOW and achieved a 99% boost in computational efficiency, making large-scale uncertainty analysis practical [123].

5.2. Strategy 2: ANNs for Parameter Estimation (Inverse Modeling)

This strategy uses an ANN to solve the challenging inverse problem of estimating key MODFLOW input parameters, such as the spatial distribution of hydraulic conductivity, from observed data [124]. This data-driven approach can replace or supplement traditional, time-consuming calibration methods [13]. The ANN offers a powerful method to map the complex, non-linear relationships between aquifer stresses, responses, and properties without a priori assumptions. A notable case study by [118] used an ANN to derive regression equations for predicting potentiometric heads based on geological and mining parameters, complementing a detailed MODFLOW sensitivity analysis of a mine complex.

5.3. Strategy 3: An ANN as an Error-Correction Model

This advanced hybrid approach uses a calibrated MODFLOW model to produce a primary, physics-based prediction. The systematic errors (residuals), calculated as the difference between the MODFLOW predictions and observed field data, are then modeled using an ANN [125]. The final, improved prediction is the sum of the MODFLOW output and the ANN-predicted error. This strategy leverages the strengths of both paradigms: the physics-based model provides the primary prediction, while the data-driven model captures complex, unmodeled dynamics and local biases present in the residuals [119]. A case study from the Bist-Doab region in Punjab, India, successfully applied this residual modeling approach to integrate the MODFLOW model with machine learning models, significantly reducing model error and improving predictions in an agriculturally stressed region [126].

Table 8. Summary of the literature on hybrid MODFLOW–ANN models.

Ref.	Study Area	Model(s) Used	Key Input Data	Findings
[30]	China	MLP, RBF, SVM	Pumping rates, recharge rates, streamflow rates, groundwater level	The RBF model excelled in accuracy and computation time during training, but the numerical model showed better generalization.
[119]	Synthetic aquifer (Argonne Lab)	MODFLOW, ANN	Hydraulic conductivity, infiltration, evapotranspiration	An error-mapping ANN is an efficient approach for estimating model uncertainty.
[127]	Poland	ANN, MODFLOW	Rainfall, river currents, irrigation, well discharge, evaporation	TLRNs (R2 = 0.958) showed higher accuracy than MLPs (R2 = 0.865) in simulating groundwater levels.
[128]	Kathajodi-Surua, Odisha	ANN, MODFLOW	Weekly groundwater level data	The ANN model provided better predictions for short-term forecasts compared to MODFLOW.
[129]	Trivandrum, India	MODFLOW, RBFNN	Recharge, evapotranspiration, pumping rate, groundwater level	The RBFNN model outperformed MODFLOW for weekly groundwater level forecasting.
[130]	Birjand Aquifer, Iran	MODFLOW, ANN, BN	Temperature, evaporation, recharge, discharge, water tables	BN models (R2 = 0.9) surpassed ANNs (R2 = 0.76) and mathematical models (R2 = 0.72).
[131]	Qazvin Plain, Iran	MODFLOW, ANN	Monthly weather, precipitation data	The DWS index indicated the aquifer’s safe yield is only 44% of the current abstraction volume.
[132]	Kabodarahang Plain, Iran	MODFLOW, ELM, WA-ELM	Hydraulic conductivity, storage coefficients, recharge coefficients	The WA-ELM model was superior for simulating groundwater levels (R2 = 0.959, NSC = 0.915).
[133]	Iran	MODFLOW, HACRES	-	Stream discharge rates are projected to decrease in the future, especially under the RCP8.5 scenario.
[134]	Iran	GMS, ANN	Monthly precipitation, groundwater level data	The ORELM AI model outperformed other AI models and the GMS numerical model (RMSE of 0.37 in training).
[135]	Iran	BF-ANN	River flow, precipitation, evaporation, groundwater level, demands	The SOS-MSA-ANN model achieved the highest sustainability index, supplying over 99% of total demands.

summarizes the key literature reviewed for these integrated hybrid approaches, providing an overview of the methodologies and findings in this emerging area.

6. Synthesis and Discussion

The integration of the physically based MODFLOW model and data-driven ANNs signals a new paradigm in how groundwater systems are simulated and managed. This systematic review has illuminated the powerful synergies that arise from their strategic combination. Hybrid approaches integrate the physical principles of numerical models with the computational efficiency of machine learning, thereby enabling more accurate, robust, and efficient hydrogeological analysis. The cumulative literature evidence from global and Indian case studies indicates that hybrid models consistently outperform their standalone counterparts. This superior performance obtained from a powerful symbiotic relationship: MODFLOW provides the physical framework, constraining the model to physically realistic solutions, while ANNs address key limitations by accelerating computations, enhancing parameterization, and correcting systematic biases.

This review has categorized the primary integration methods into three core strategies: surrogate modeling, intelligent parameterization, and error correction. The choice of strategy depends critically on the scientific question, data availability, and computational resources. This strategic diversity underscores the maturity of the field and highlights the need for modeling teams to possess expertise in both hydrogeology and data science.

7. Conclusions and Future Research Directions

This systematic review confirms that the integration of MODFLOW models and ANNs provides a more comprehensive and accurate depiction of aquifer systems than either method alone. By systematically categorizing the literature into a unique classification of integration strategies, we have provided a structured framework for understanding and advancing the field.

Although the progress in hybrid modeling has been considerable, it represents the early stages of a rapidly advancing field with vast potential. To realize the full potential of these integrated models, future research should focus on several key areas:

• Explainable AI (XAI) and Physics-Informed Neural Networks (PINNs): The most significant barrier to broader adoption remains the black box problem. Future research must prioritize the development of techniques like PINNs, which bake physical laws directly into the network architecture, to make these models more transparent and trustworthy.
• Scalability and High-Performance Computing (HPC): A major challenge is scaling these hybrid approaches to large regional or national scales, which will require leveraging HPC resources to handle the massive datasets and complex training procedures involved.
• Real-Time Data Assimilation: Future work should focus on developing methods to dynamically assimilate real-time data streams from sources like remote-sensing satellites and IoT-enabled sensors into these hybrid models, enabling a shift from static to dynamic, adaptive forecasting systems.

By pursuing these research directions, the scientific community can continue to build upon the strong foundation of MODFLOW–ANN integration, creating the next generation of groundwater models that are not only more powerful but also more transparent, reliable, and integral to securing our global water future.