Generating 3D Geothermal Maps in Catalonia, Spain Using a Hybrid Adaptive Multitask Deep Learning Procedure

Abstract

Mapping the subsurface temperatures can efficiently lead to identifying the geothermal distribution heat flow and potential hot spots at different depths. In this paper, an advanced adaptive multitask deep learning procedure for 3D spatial mapping of the subsurface temperature was proposed. As a result, predictive 3D spatial subsurface temperatures at different depths were successfully generated using geolocation of 494 exploratory boreholes data in Catalonia (Spain). To increase the accuracy of the achieved results, hybridization with a new modified firefly algorithm was carried out. Subsequently, uncertainty analysis using a novel automated ensemble deep learning approach for the predicted temperatures and generated spatial 3D maps were executed. Comparing the accuracy performances in terms of correct classification rate (CCR) and the area under the precision–recall curves for validation and whole datasets with at least 4.93% and 2.76% improvement indicated for superiority of the hybridized model. According to the results, the efficiency of the proposed hybrid multitask deep learning in 3D geothermal characterization to enhance the understanding and predictability of subsurface spatial distribution of temperatures is inferred. This implies that the applicability and cost effectiveness of the adaptive procedure in producing 3D high resolution depth dependent temperatures can lead to locate prospective geothermally hotspot active regions.

1. Introduction

Access to energy resources is a critical worldwide issue. From this point of view, renewable power is emerging as an innovative cost-effective and clean source of energy for the future. Accordingly, the renewable resources are increasingly displacing fossil fuels in the power sector because of their capability to reduce carbon emissions and other types of pollution. However, several marketed renewable resources (e.g., biomass and large hydroelectric dams) due to some problematic tradeoffs may not be suitable to the geoenvironmental concerns [1]. In the field of renewables, geothermal is always available to be tapped and thus in comparison with other resources provides a reliable source of power [2]. Moreover, the low carbon intensity than the solar photovoltaic makes it a useful tool against the advance of climate change. Furthermore, versatility of geothermal resources dedicates particularly useful for promoting economic diversification [3,4].

The view of the increasing trend of the consumed energy in Europe and subsequently worldwide dependency on the external sources attractively moves toward developing the use of renewable energies and, in particular, geothermal resources as an appropriate solution [5,6]. Referring to Chamorro et al., (2014) [7], Spain can significantly be benefited from the high capacity of the natural geothermal resources. This is because in the Iberian Peninsula, the temperature can reach high values at shallow depths. Accordingly, in recent years using shallow geothermal resources have depicted steady growth and popularity in the construction subsector, whereas in power generation due to associated problem with electricity, unequal progress was reported [8,9].

The temperature of geothermal resources originating from the continuously produced heat within the earth can be classified into high (T > 225 °C), intermediated (125–225 °C), and low (T < 125 °C) systems [10]. To achieve this source of energy, the knowledge on subsurface geological hot spots for more precise drilling to access the target temperature is of great importance [11]. Therefore, to assess the well productivity, several parameters such as morphology and temperature of the ground, geothermal gradient, porosity, permeability, fluid salinity, thermal conductivity, and specific heat capacity at various depths play a critical role [12]. However, all this information often is not accessible [13] and also continuous or periodically monitoring the equipped test boreholes with temperature sensors is a time-consuming and costly procedure [4]. This is the reason why the geoengineering characteristics depend on the scale of the project are often approximated with different techniques and computer modelling approaches [14,15,16,17]. Producing 3D conceptual shallow geothermal potentials [18,19], utilizing GIS [20,21,22], spatial data analysis [23,24,25], applying numerical technique [26,27,28,29], integrated of different geophysical prospecting techniques such as magnetotelluric [30,31,32,33,34], gravity [33,35], seismic [31,33], and electrical resistivity [31,36,37], as well as evident geological characteristics [38,39] are some of the carried efforts in Spain, Chile, Pakistan, Iran, India, Nigeria, Indonesia, Denmark, China, Thailand, Italy, Taiwan, Finland and Japan. However, simulating the geothermal resources using numerical techniques due to complexity of the model preparation (natural state properties of the rocks and geothermal system), description of the realistic problem and evaluation of the results as well as inability in providing any insight into generalizations is a very time-consuming task that demands extensive experience. In case of GIS, learning curve can be long where the spatial relationships do not lead to absolute solutions and also the integration with traditional map is difficult [40,41,42]. Such drawbacks in generating high resolution 3D maps due to dedicating more flexibility but higher computational and analytical capabilities can be handled by artificial intelligence (AI) approaches. The skilled AI-based models in geoengineering problems were used to tackle the difficulties in handling the big data [43] and provide physically meaningful relationships within geo-data [44,45,46]. Accordingly, applicability of the AI techniques in the form of artificial neural network, machine/deep learning, evolutionary algorithms, and hybrid structures in producing the predictive 3D subsurface models have been highlighted [46,47,48,49,50,51]. Due to characterized features in creating transferable solutions and learnability from high-level data attributes [52] the feasibility of AI techniques in geothermal modeling [53,54] and compared performance by field prospecting methods [55,56] have been notified in several studies dealing with predicting the location of hot spot structures [57,58,59,60], estimating the temperature distribution [61,62], and potential of geothermal production associated with geological data [63,64].

Referring to literature reviews, the AI models can be optimized through metaheuristic algorithms to find the most proper solutions relative to a set of prioritized criteria or constraints [65,66,67,68]. However, the optimizing performance of these algorithms due to analytical shortcomings cannot be guaranteed [65,69]. This limitation of metaheuristic algorithms with growing interested in optimization methods can be covered using modification process to improve the performance and prevent from computational costs of a rework [69,70,71].

The firefly algorithm (FA) [72] is a developed swarm optimization method based on the attractiveness of fireflies, but suffers from slow convergence and getting trapped in local optimum for multimodal problems [73]. In this paper a new developed version of modified FA by Abbaszadeh Shahri et al., 2022a [69] is used.

In this point of view, Spain, despite the access to high potential of different types of geothermal resources is still far from achieving a generalized utilizing of these renewable systems [74]. However, following the European initiatives, based on the 2011–2020 renewable energy plan, Spain is also working on promising geothermal areas for both power production and direct applications [75]. Due to the lack of worldwide characterized information of subsurface geothermal hotspots [8], developing the modelling techniques for evaluation, and utilizing these resources critically should be considered as one of the most prolific tasks for contributing to the global sustainability [18,76,77,78]. Moreover, the information of subsurface soils often is acquired from the vertical sparse exploratory boreholes in which laterally spatial distribution of predicted parameter is a difficult task [46,47,49]. This implies that evaluating the models aiming to identify the possible hotspots can lead to utilize and decrease the available gaps of this resource with respect to other European nations and would allow Spain to reduce its foreign energy dependency. Such demands crucially motive for developing new computational modelling techniques leading to new frameworks for the future expansion of this energy.

Despite the demonstrated more precise results in hybridized AI techniques with the high-level metaheuristic optimization algorithms [69], no distinguished work dealing on developing multi-task predictive models through platform of intelligence systems in geothermal application is available. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off [79] and thus has received considerable attention in real-world problems. In such learning schemes multiple tasks are solved jointly and sharing inductive bias between tasks. Therefore, referring to the above-mentioned concerns and the progressively emerged interest in developing 3D digital models, an adaptive hybridized multi-task deep learning AI procedure for generating spatial subsurface temperature at different depths in Catalonia, Spain, was developed. Hybridizing process was carried out through a new version of modified firefly algorithm (MFA). The modelling procedure was executed through 496 numbers of sparse data comprising latitude, longitude, elevation, and surface temperature. Accordingly, the temperatures at depths 50 and 150 m were predicted, and the model then was setup to provide estimation for 120 and 180 m, respectively. The evaluated receiver operating characteristic (ROC) supplemented by error analysis showed the applicability and cost effectiveness of the adopted multitask procedure in producing high resolution depth dependent subsurface temperature maps for the study area. Subsequently, an uncertainty analysis using an introduced state-of-the-art approach for the predicted temperature and generated spatial maps were conducted.

2. Materials and Methods

2.1. Study Area and Acquired Datasets

Catalonia is a province of Spain located at the north-east of the Iberian Peninsula, in the western Mediterranean area with a diverse range of geomorphological features from mountainous to coastal landscapes [80,81]. This study is focused in an area of 7942 km² in the northeastern part of Catalonia, as presented in Figure 1. The northern domain is a mountainous territory corresponding to the eastern part of the Pyrenees and the southern limb tie in with the Catalan Coastal Ranges that are parallel to the Mediterranean shoreline. The area is made up by a Paleozoic continental crust affected by extensive sedimentary basins during Mesozoic and Neogene and a compressive basin of Paleogene age coeval with the development of the Pyrenees and the Catalan Coastal Ranges [82,83].

Previous carried out research implied on ideal geothermal inquiry in several regions of this area such as Vallès, Empordà, La Selva, Penedès, Fossa d’Olot, Plana de Vic, Depressió Central (Lleida), and Maresme. Accordingly, in this study, a number of 496 stochastic datasets including longitude (X), latitude (Y), elevation (Z) and surface temperature (Ts) were derived from the database of the Catalonia Cartographic and Geological Institute (ICGC) [84,85]. The used database in the current paper was constructed from the compiled annually time-dependent information provided by ICGC for the year of 2021 at each measuring station or control point. The acquired datasets for further procedure were randomized and split into 65%, 20% and 15% to establish the training, testing, and validation sets and after compiling were normalized within [0, 1] interval to increase the learning speed and model stability.

2.2. Deep Neural Learning Structure

Multitask learning can increase the generalization of deep neural learning structures (DNLS) by employing domain information contained in the training inputs of related tasks as an inductive bias. In comparison to training the models independently, this learning procedure aims to tackle multiple tasks at the same time to enhance efficiency and prediction accuracy [79,86]. This implies on performing parallel learning with a shared representation, in which each task can help other tasks be learned better [87,88,89].

As shown in Figure 2, DNLS is a subcategory of AI techniques with multiple layers in which without being explicitly can scan the data to search combinable features for faster learning. This ability indicates for ameliorate feature extraction over machine learning and thus supreme performance of DNLS with unstructured data (e.g., texts, pictures, pdf, etc.) as well as exploring new complex attributes that humans might miss [90].

In this structure, the received input signals (x₁, x₂, …, x_n) are passed to the hidden layers and then to the next senior level using adopted weights (w_ij, w_jk):

$$\stackrel{x_1, \dots x_n}{\overbrace{Input}} \stackrel{w_{ij}}{\to } \stackrel{o_j^z}{\overbrace{\underset{ }{Hidden layers}} \stackrel{w_{jk}}{\to }}\stackrel{ Y}{\overbrace{Output}}$$

(1)

Referring to Figure 2, the output of the jth neuron in the zth hidden layer at the tth iteration, $o_j^z\left(t\right)$, subjected to activation function, $f_j^z$, is defined as:

$$o_j^z\left(t\right)=f_j^z\left({{\displaystyle \sum }}_{i=1}^{n_z-1}{w}_{ij}^z{x}_i^{z-1}\left(t\right)+b_j^z\right) \left(j\le n_z\right)$$

(2)

where n_z shows the number of neurons in the zth layer, and $b_j^z$ denotes the bias which shifts the summed signals received from the neuron.

The outcome of the lth neuron in the mth output layer after t iteration ($Y_l\left(t\right)$), is then calculated using the updated weight by:

$$Y_l\left(t\right)={{\displaystyle \sum }}_{i=1}^{n_m-1}{w}_{ij}^m{x}_i^{m-1}\left(t\right) \left(l\le n_{\mathrm{o}}\right)$$

(3)

where n_o represents the number of neurons in the output layer.

Accordingly, the error of model for entire network (E (t)) and predicted values (e (t)) are expressed as:

$$E\left(t\right)=\frac{1}{2}{{\displaystyle \sum }}_{j=1}^n{\left(d_j\left(t\right)-o_j^k\left(t\right)\right)}^2$$

(4)

$$e\left(t\right)=y-Y\left(t\right)$$

(5)

where d_j (t) denotes the desired output of neuron j at the tth iteration and y shows the actual output.

In each iteration, then the weights are updated through the learning rate to minimize the prediction error of using:

$$\Delta w\left(t\right)=-{\eta }_w(\frac{\partial E\left(t\right)}{\partial w_{old}})$$

(6)

where ${\eta }_w$ represent the learning rate.

2.3. The Used Modified FA (MFA)

The original FA [72] has been formulated using the attractiveness of fireflies, their brightness and adjacent distance.

Table 1. Required parameters to tune the FA.

	Description	Parameter	Advised Ranges	Notation
	brightness	I	-	objective function
	attractiveness	β	-	-
	distance between two fireflies i, j	rij	-	-
	absorption coefficient	γ	[0.1–10]	-
	trade off constant in randomized movement	α	[0, 1]	randomization parameter
	attractiveness at distance 0 (rij = 0)	β0	normally 1	-
	number of generations	Gen	-	iteration
	problem dimension	D	-	dimension
	number of fireflies	n	-	population size
β, β0, α and γ also can be organized based on parametric investigations.

shows the involved parameters in FA that depending on the problem should properly be tuned through trial-error procedure.

The concept of this algorithm is based on the I as the objective function in such way that a firefly is attracted by the brighter one (new solution). As a result of moving toward each other, the distance between the fireflies is updated. Accordingly, the position of the moved firefly after t iteration and implemented update step size of (x_j − x_i) reflects a new solution ($x_i^{new}$) that further should be evaluated by the fitness function (FT) in the population by:

$$x_i^{new}=x_i^t+{\beta }_0{e}^{-\gamma r_{ij}^2}\left(x_j-x_i\right)+\alpha \left(rand-0.5\right)$$

(7)

where i, j denotes the index of fireflies and the rand function corresponds a random number of solutions. Using this iterative process only one solution with the lowest FT will be kept [91]. Therefore, each new generated solution, $x_i^{new}$ showing the updated location of firefly is governed by α and γ. Accordingly, the smaller γ, the faster convergence history but the greater β between fireflies. On the other hand, the larger α connote to increasing the range of random motion of fireflies and thereby the slower convergence. In the modified version presented by [69], Equation (7) was updated through the brightness expectation value, using:

$$x_i^{modified}=x_i+{\beta }_0{e}^{-{\gamma }_t{r}_{ij}^2}\left(x_j-x_i\right)+{\alpha }_t{r}_{ij}\left(rand-0.5\right)$$

(8)

Accordingly, α and γ then adaptively are tuned and updated using the variance of the population of brightness (Var (I)) by:

$$\{\begin{array}{c}{\gamma }_t={\gamma }_0+e^{-k.Var\left(I\right)}\left({\gamma }_u-{\gamma }_0\right)\\ {\alpha }_t={\alpha }_0-e^{-k.Var\left(I\right)}\left|({\alpha }_u-{\alpha }_0)\right|\\ {\alpha }_0>{\alpha }_u,{\gamma }_u>{\gamma }_0,k>0\end{array}$$

(9)

where, subscripts 0 and u denotes the initial and ultimate values. Using this modification, the convergence speed and the computational time are boosted and strengthened [69].

3. Developing Hybrid Adaptive Procedure

The hybridizing procedure benefits from integration of different predictive AI model with optimization methods to capture more accurate output and thus higher performance. Therefore, adopting appropriate procedure to apprehend an optimum multitask topology for predictive unit is critical to avoid from over-fitting problem, early convergence and not getting stuck in local minima. Figure 3 depicts the block-based hybrid adaptive DNLS-MFA procedure subjected to iterative constructive technique that using several inner nested loops was programmed in C++. In this approach, 80% of randomized data is used for training. Through the adopted k-fold checking (here set for 10 times), the data then internally are re-randomized into 60% and 20% for training and testing. The remained 20% of unseen data was used for model validation. This iterate-based adaptive procedure was configured for leading to an optimum multitask DNSL with a proper adjustment of the internal characteristics and corresponding hyper parameters. To reduce the computational time, the number of maximum hidden layers and used neurons were limited to 3 and 30, respectively. The learning rate also was managed within [0.001, 1.000] interval with a step size of 0.05. The first priority to terminate the training process is to achieve the minimum network root mean square error (RMSE) and if not satisfied then the number of iterations (t) will active as set for 500 in this study.

Figure 4a shows the results of series dynamically monitored and analyzed architectures depend upon the implemented training algorithm (TA), learning rate and activation function (AF). According to Figure 4b, the DNLS topology with structure of 4-15-5-2 trained by limited memory quasi-Newton (LMQN) subjected to hyperbolic tangent (Hyt) activation function can be selected as optimal. In the given topology, 4 denotes the number of used inputs (X, Y, Z, Ts), 15 and 5 express the number of managed neurons in first and second hidden layers and 2 is assigned to the multiple outputs comprising the temperature at depths 50, 150 m (T50, T150), respectively.

As presented in Figure 3, the selected optimum topology (Figure 4b) is hybridized with the MFA. Referring to Table 1 and Equations (7)–(9), the updated location of firefly should be tuned using α, β and γ. However, appropriate setting of these parameters is not easy task. The most representative values of α, β and γ then were captured through parametric regularizing procedure. Figure 5a shows the result of a series of analyses subjected to RMSE with two fixed parameters and one variable. The results showed that the values of 1, 0.5, 0.2, 0.5 corresponding to γ, β, α, β₀ (Figure 5a) and 30 for population of fireflies (Figure 5b) can be the optimal. Accordingly, the predictability of the model using adaptive DNLS (Figure 5c,d) and the hybrid DNLS-MFA (Figure 5e,f) were presented and compared.

Traditional 3D modelling techniques are subjective and limited to the knowledge and experiences of experts in the selection of assumptions and parameters. For subsurface geothermal purposes, therefore, creating 3D depth-dependent digitized spatial predictive maps using identified hybrid optimum DNLS model play an important priority. As a result, for the study area, the created 3D maps using the hybrid DNLS-MFA at the surface and depth of 50 and 150 m are presented (Figure 6a–c). The applicability of the DNLS-MFA then was examined using unlabelled data for two other depths. Accordingly, the elevation was replaced by converted depths for 120 and 180 m with respect to the ground surface elevation with the same used input data. The model then was trained for the whole datasets through the saved weight database and the visualized results were reflected in Figure 6d,e. According to the documented results by Colmenar-Santos et al. (2016) [92] from the report of Institute for the Diversification and Saving of Energy (IDEA), the range of predicted subsurface temperatures show appropriate compatibilities. The predicted subsurface using the applied model at depth of 150 m dedicated about 33 °C, where considering the nonlinearity and heterogeneity it is expected to fall around 70 at 300 m depth. Therefore, referring to [92], the subsurface temperature in the study area corresponding to the depths between 300–2500 m will fall within the interval of [70 °C, 140 °C].

4. Discussion and Validation

Generally, the statistical error metrics are used to evaluate the performance of the complex models through pair-wise-matched of observations and predictions [93]. In this study, as presented in

Table 2. Evaluated error metrics of the predicted temperatures using validation datasets.

	Optimum DNLS		Hybrid DNLS-MFA
	T50	T150	T50	T150
R2	0.87	0.86	0.92	0.91
RMSE	0.49	1.00	0.37	0.79
MAPE	2.40	4.00	1.80	3.2
IA	0.96	0.96	0.98	0.97

the models were assessed by means of the mean absolute percentage error (MAPE), RMSE, index of agreement (IA) [94] and R². The better performance was selected by higher IA, R² accompanying with lower MAPE and RMSE. Table 2 reflects the comparison of the applied metrics for the 15% of unseen randomized validation datasets through the weight database.

Using confusion matrix [95], the predictability performance of developed models is analyzed, where each diagonal entry of [a_ij] as the number of records for ith and jth category of target and corresponding network output would be non-zero. In this study, the multiclass confusion matrixes for optimum and hybridized DNLS models using validation datasets were established (

Table 3. Confusion matrix of optimum models using validation datasets.

Target Output	Output of Optimum DNLS: 50 m Depth												Results
	<12.01	12.01–12.69	12.69–13.38	13.38–14.06	14.06–14.75	14.75–15.43	15.43–16.11	16.11–16.80	16.80–17.48	17.48–18.17	18.17–18.85	>18.85	Total	True	False
12.01–12.69		2		1									3	2	1
12.69–13.38			0										0	0	0
13.38–14.06				1									1	1	0
14.06–14.75					1								1	1	0
14.75–15.43						2	1						3	2	1
15.43–16.11						1	7	1					10	7	3
16.11–16.80								16	1	1			18	16	2
16.80–17.48								1	18	2			21	18	3
17.48–18.17									1	8	1		10	8	2
18.17–18.85										1	5	1	7	5	2
Note	0	2	0	2	1	3	8	18	20	12	6	1	74	60	14
	Output of Hybrid DNLS: 50 m Depth												Results
12.01–12.69		2	1										3	2	1
12.69–13.38			0										0	0	0
13.38–14.06				1									1	1	0
14.06–14.75					0	1							1	0	1
14.75–15.43						3							3	3	0
15.43–16.11						1	8	1					10	8	2
16.11–16.80								17	1				18	17	1
16.80–17.48									20	1			21	20	1
17.48–18.17									1	8	1		10	8	2
18.17–18.85											6	1	7	6	1
Note	0	2	1	1	0	5	9	17	22	9	7	1	74	65	9
Target Output	Output of Optimum DNLS: 150 m Depth												Results
	<13.66	13.66–14.73	14.73–15.8	15.8–16.87	16.87–17.94	17.94–19.01	19.01–20.08	20.08–21.15	21.15–22.22	22.22–23.29	23.29–24.36	>24.36	Total	True	False
13.66–14.73	1	1	1										3	1	2
14.73–15.8			3	1									4	3	1
15.8–16.87			1	4		1							6	4	2
16.87–17.94					4		1						5	4	1
17.94–19.01					1	8		1					10	8	2
19.01–20.08					1	1	10	1					13	10	3
20.08–21.15							1	10		1			12	10	2
21.15–22.22							1		8				9	8	1
22.22–23.29								1		5	1		7	5	2
23.29–24.36											4	1	5	4	1
Note	1	1	5	5	6	10	13	13	7	7	5	1	74	57	17
	Output of Hybrid DNLS: 150 m depth												Results
13.66–14.73	1	2											3	2	1
14.73–15.8			3	1									4	3	1
15.8–16.87			1	4	1								6	4	2
16.87–17.94					4	1							5	4	1
17.94–19.01						9	1						10	9	1
19.01–20.08						1	11	1					13	11	2
20.08–21.15								11		1			12	11	1
21.15–22.22								1	8				9	8	1
22.22–23.29									1	5	1		7	5	2
23.29–24.36											3	1	5	3	2
Note	1	2	4	5	6	10	12	13	9	6	4	2	74	60	14

). The cells with value of 0 shows there is no predicted result correspond to target output. This can be an indicator of appropriate predictability of developed models. Accordingly, the compared qualitative characteristics in classification tasks using correct classification rate (CCR) (

Table 4. Comparing the CCR and model improvement using validation data.

Model	CCR (%)	Improved Progress
Optimum DNLS-T50	81.1	6.24%
Hybrid DNLS-T50	86.5
Optimum DNLS-T150	77.1	4.93%
Hybrid DNLS-T150	81.1

) showed at least 4.2% improvement in the predictability level of hybrid DNLS than the optimum topology.

The presented confusion matrix (Table 3) then was used to plot the area under the curve of receiver operating characteristics (AUC_ROC). The ROC is a 2D graphical probability approach to assess the overall performance of a model, where the greater AUC the higher capability in diagnosed classes [96,97]. Precision shows the true predictions in each class and recall reflects the ability of model in identifying the actual positives. Therefore, the predictability of a model in a full picture at different thresholds can be quantified using the precision–recall ROC curves. Referring to Figure 7, the achieved accuracies of 90.7% and 86.3% using hybrid DNLS-MFA for T50 and T150 demonstrated more reliable outputs than optimum DNLS.

In computational systems the uncertainty analysis for the new individual upcoming observations can be estimated using prediction interval (PI) [98]. One of the key benefits of PI is referred to dedicating a range of weights allowing for insight into how accurate the predicted weight is likely to be [99]. The PI is always wider than a confidence interval because it considers the uncertainty in both predicting the population mean and the random variation of the individual values [100]. In this study, the PI of the hybrid DNLS-MFA at the level of 95% was estimated using a state-of-the-art automated random deactivating weight approach [101], as shown in Figure 8. The applied approach [101] subjected to hybrid DNLS-MFA for T50 and T150 showed narrower distribution of PI, leading to the identification of the potential hot spot sub-areas with lower uncertainty.

5. Conclusions

Mapping the subsurface temperature in complex structural settings using advanced DNLS can dedicate a viable tool for exploration analyses and thus drilling phases. Refer to this motivation, an adaptive hybrid multitask DNSL-MFA procedure for producing the 3D predictive spatial maps of the temperature-at-depths was developed and applied on 494 geo-location and surface temperature datasets in a part of Catalonia, Spain. Compared with DNLS, the predicted maps at depths of 50 and 150 m using the introduced hybrid DNSL-MFA scheme showed 90.7% and 86.3% accuracy performances leading to 6.24% and 4.93% improvements, respectively. The evaluations then were supplemented by error criteria and uncertainty analysis, where the narrower distribution of PI in hybrid DNLS-MFA showed higher reliability in identifying the most compatible potentials in the study area. Accordingly, the predictability of the hybrid model was then examined with unlabelled data at depths 120 and 180 m, in which the created 3D maps showed appropriate responses to categorized subsurface temperatures. Using the generated 3D visualized maps not only the spatial extension of the interested areas at investigated depth are recognized but also facilitate the interpretability of subsurface heating conditions and, consequently, reducing the geothermal exploration costs. This implies on applicability of produced maps in reflecting the most favorable hotspot locations for further geothermal analyses and thus better site characterizing for field and real-world applications. The presented hybrid DNLS-MFA is preferred because the produced digitized 3D spatial maps can be updated using new geoscientific data to improve serving for deeper insights into the geothermal resource systems. However, more knowledge on potential subsurface hot spots is needed to enhance geothermal energy use and public awareness.