Deep learning models for groundwater level prediction based on delay penalty

Miami-Dade County, FL, has complex hydrological and water management conditions, creating challenges for predicting groundwater levels. Due to the potential impacts of increasing sea level and changes in rain patterns on flooding and saltwater intrusion, it is essential to be able to accurately predict groundwater levels and to understand the drivers of groundwater levels. The method traditionally used to predict groundwater levels in south Florida and elsewhere is through the implementation of a numerical model. This research looks at machine learning techniques as an alternative method to provide improved predictions of groundwater levels. Extreme gradient boosting is one of the machine learning techniques that uses algorithms to train a model by identifying hidden patterns and relationships between groundwater level drivers and groundwater levels. The accuracies of the extreme gradient boosting model and a numerical model were compared by computing the root mean square error as a model performance measure. Comparing these two methods showed that the extreme gradient boosting model had better accuracy in predicting groundwater levels at the majority of groundwater monitoring sites. Furthermore, comparison of these two models helped us to identify problematic areas where both models performed poorly and narrow down the factors that could cause this poor model performance. Finally, the extreme gradient boosting method gave the importance of each feature included among the potential groundwater level drivers, including the ranked importance of a particular factor and its lag time, at each of the considered groundwater level monitoring sites.

Abstract. The application of machine learning (ML) including deep learning models in hydrogeology to model and predict groundwater level in monitoring wells has gained some traction in recent years. Currently, the dominant model class is the so-called single-well model, where one model is trained for each well separately. However, recent developments in neighbouring disciplines including hydrology (rainfall–runoff modelling) have shown that global models, being able to incorporate data of several wells, may have advantages. These models are often called “entity-aware models“, as they usually rely on static data to differentiate the entities, i.e. groundwater wells in hydrogeology or catchments in surface hydrology. We test two kinds of static information to characterize the groundwater wells in a global, entity-aware deep learning model set-up: first, environmental features that are continuously available and thus theoretically enable spatial generalization (regionalization), and second, time-series features that are derived from the past time series at the respective well. Moreover, we test random integer features as entity information for comparison. We use a published dataset of 108 groundwater wells in Germany, and evaluate the performance of the models in terms of Nash–Sutcliffe efficiency (NSE) in an in-sample and an out-of-sample setting, representing temporal and spatial generalization. Our results show that entity-aware models work well with a mean performance of NSE >0.8 in an in-sample setting, thus being comparable to, or even outperforming, single-well models. However, they do not generalize well spatially in an out-of-sample setting (mean NSE <0.7, i.e. lower than a global model without entity information). Strikingly, all model variants, regardless of the type of static features used, basically perform equally well both in- and out-of-sample. The conclusion is that the model in fact does not show entity awareness, but uses static features merely as unique identifiers, raising the research question of how to properly establish entity awareness in deep learning models. Potential future avenues lie in bigger datasets, as the relatively small number of wells in the dataset might not be enough to take full advantage of global models. Also, more research is needed to find meaningful static features for ML in hydrogeology.

The precise forecasting of groundwater levels significantly influences plant growth and the sustainable management of ecosystems. Nonetheless, the non-stationary characteristics of groundwater level data often hinder the current deep learning algorithms from precisely capturing variations in groundwater levels. We used Variational Mode Decomposition (VMD) and an enhanced Transformer model to address this issue. Our objective was to develop a deep learning model called VMD-iTransformer, which aims to forecast variations in the groundwater level. This research used nine groundwater level monitoring stations located in Hangjinqi Ecological Reserve in Kubuqi Desert, China, as case studies to forecast the groundwater level over four months. To enhance the predictive performance of VMD-iTransformer, we introduced a novel approach to model the fluctuations in groundwater levels in the Kubuqi Desert region. This technique aims to achieve precise predictions of the non-stationary groundwater level conditions. Compared with the classic Transformer model, our deep learning model more effectively captured the non-stationarity of groundwater level variations and enhanced the prediction accuracy by 70% in the test set. The novelty of this deep learning model lies in its initial decomposition of multimodal signals using an adaptive approach, followed by the reconfiguration of the conventional Transformer model’s structure (via self-attention and inversion of a feed-forward neural network (FNN)) to effectively address the challenge of multivariate time prediction. Through the evaluation of the prediction results, we determined that the method had a mean absolute error (MAE) of 0.0251, a root mean square error (RMSE) of 0.0262, a mean absolute percentage error (MAPE) of 1.2811%, and a coefficient of determination (R2) of 0.9287. This study validated VMD and the iTransformer deep learning model, offering a novel modeling approach for precisely predicting fluctuations in groundwater levels in a non-stationary context, thereby aiding sustainable water resource management in ecological reserves. The VMD-iTransformer model enhances projections of the water level, facilitating the reasonable distribution of water resources and the long-term preservation of ecosystems, providing technical assistance for ecosystems’ vitality and sustainable regional development.

Forecasting of groundwater levels is very useful for planning integrated management of groundwater and surface water resources in a basin. In the present study, artificial neural network models have been developed for groundwater level forecasting in a river island of tropical humid region, eastern India. ANN modeling was carried out to predict groundwater levels 1 week ahead at 18 sites over the study area. The inputs to the ANN models consisted of weekly rainfall, pan evaporation, river stage, water level in the drain, pumping rate and groundwater level in the previous week, which led to 40 input nodes and 18 output nodes. Three different ANN training algorithms, viz., gradient descent with momentum and adaptive learning rate backpropagation (GDX) algorithm, Levenberg–Marquardt (LM) algorithm and Bayesian regularization (BR) algorithm were employed and their performance was evaluated. As the neural network became very large with 40 input nodes and 18 output nodes, the LM and BR algorithms took too much time to complete a single iteration. Consequently, the study area was divided into three clusters and the performance evaluation of the three ANN training algorithms was done separately for all the clusters. The performance of all the three ANN training algorithms in predicting groundwater levels over the study area was found to be almost equally good. However, the performance of the BR algorithm was found slightly superior to that of the GDX and LM algorithms. The ANN model trained with BR algorithm was further used for predicting groundwater levels 2, 3 and 4 weeks ahead in the tubewells of one cluster using the same inputs. It was found that though the accuracy of predicted groundwater levels generally decreases with an increase in the lead time, the predicted groundwater levels are reasonable for the larger lead times as well.

The Ardebil plain, which is located in northwest Iran, has been faced with a recent and severe decline in groundwater level caused by a decrease of precipitation, successive long-term droughts, and overexploitation of groundwater for irrigating the farmlands. Predictions of groundwater levels can help planners to deal with persistent water deficiencies. In this study, the support vector regression (SVR) and M5 decision tree models were used to predict the groundwater level in Ardebil plain. The monthly groundwater level data from 24 piezometers for a 17-year period (1997 to 2013) were used for training and test of models. The model inputs included the groundwater levels of previous months, the volume of entering precipitation into every cell, and the discharge of wells. The model output was the groundwater level in the current month. In order to evaluate the performance of models, the correlation coefficient (R) and the root-mean-square error criteria were used. The results indicated that both SVR and M5 decision tree models performed well for the prediction of groundwater level in the Ardebil plain. However, the results obtained from the M5 decision tree model are more straightforward, more easily applied, and simpler to interpret than those from the SVR. The highest accuracy was obtained using the SVR model to predict the groundwater level from the Ghareh Hasanloo and Khalifeloo piezometers with R = 0.996 and R = 0.983, respectively.

Drug repurposing in the context of neuroimmunological (NI) investigations is still in its primary stages. Drug repurposing is an important method that bypasses lengthy drug discovery procedures and focuses on discovering new usages for known medications. Neuroimmunological diseases, such as Alzheimer’s, Parkinson’s, multiple sclerosis, and depression, include various pathologies that result from the interaction between the central nervous system and the immune system. However, the repurposing of NI medications is hindered by the vast amount of information that needs mining. We previously presented Adera1.0, which was capable of text mining PubMed for answering query-based questions. However, Adera1.0 was not able to automatically identify chemical compounds within relevant sentences. To challenge the need for repurposing known medications for neuroimmunological diseases, we built a deep neural network named Adera2.0 to perform drug repurposing. The workflow uses three deep learning networks. The first network is an encoder and its main task is to embed text into matrices. The second network uses a mean squared error (MSE) loss function to predict answers in the form of embedded matrices. The third network, which constitutes the main novelty in our updated workflow, also uses a MSE loss function. Its main usage is to extract compound names from relevant sentences resulting from the previous network. To optimize the network function, we compared eight different designs. We found that a deep neural network consisting of an RNN neural network and a leaky ReLU could achieve 0.0001 loss and 67% sensitivity. Additionally, we validated Adera2.0’s ability to predict NI drug usage against the DRUG Repurposing Hub database. These results establish the ability of Adera2.0 to repurpose drug candidates that can shorten the development of the drug cycle. The workflow could be download online.

The dynamic behavior of groundwater flow and salt transport is affected by tide and pumping in coastal multilayered aquifers. In this paper, two groups of experiments were conducted considering different constant head inland boundaries. The fluctuation of the groundwater level and the process of seawater intrusion in the multilayered aquifers were observed. A two-dimensional SEAWAT model is developed to simulate the seawater intrusion to coastal aquifers under the influences of tidal fluctuation and groundwater exploitation. The hydrogeological parameters in the model are calibrated by the records of the groundwater level and salinity measurements. The results showed that the simulated groundwater level and salt concentration match the observation well. The groundwater level has the characteristics of periodic fluctuation with tide. The lag time of the groundwater level fluctuation in each monitoring point increases slightly with the increasing distance from the saltwater chamber. For the low tide, the inland freshwater recharge has main effect on groundwater level fluctuation. The rising tide has a negative effect on the drawdown of the groundwater level induced by pumping. For the high tide, the tide plays a major role on groundwater level fluctuation, compared with the inland freshwater recharge. Compared with the condition of high head of inland recharge, larger saltwater intrusion lengths and area have been observed and simulated in the aquifer, which means that faster inland motion of the seawater wedge would occur when the inland recharge is small in the coastal aquifers. It revealed that inland recharge plays a major role in the seawater intrusion for the same pumping rate of groundwater in different seasons. The analysis provides insights into how the tide fluctuation, groundwater pumping, and inland recharge effect on the area and rates of seawater intrusion.

Jeju Island is the largest island in South Korea. Recently, extensive groundwater abstraction has been reported from the shallow aquifer in the northeast region of the island. This study simulated the freshwater resources of the aquifer to estimate the sustainability of groundwater use on Jeju Island in terms of its vulnerability to seawater intrusion. Three-dimensional finite-difference numerical groundwater models were simulated using the MODFLOW-family code SEAWAT. Precise and recent groundwater level and multi-depth salinity data obtained from the study site were used for model calibration; the simulated results showed good agreement with the observed data. SEAWAT was used to delineate the current seawater-freshwater interface to quantitatively estimate the coastal fresh groundwater resources. Future stress scenarios were also simulated in response to increased pumping and various changes in the recharge. The results showed that current groundwater use in the coastal aquifer did not induce seawater intrusion in the coastal aquifer, but seawater intrusion will occur if the dry season continues for the next ten years. The vulnerability assessment based on the predicted groundwater levels and ion concentrations using numerical simulations suggests future vulnerability in the aquifer; therefore, continuous assessment and visualization of the aquifer sustainability is vital. Future projections by the integrated SEAWAT simulation and GALDIT assessment showed that an increase in groundwater pumping may escalate the vulnerability status of coastal groundwater resources from moderate to high in some areas of the study site, by inducing lateral seawater intrusion in deeper areas of the unconfined aquifer.

Based on the hydrogeological perspective, the variation in the groundwater level (W) was selected as the analysis factor, and the rainfall changes and groundwater exploitation (QGE) were considered to be the influencing factors. The influence of the two factors on W in the northern Huangqihai Basin was analyzed qualitatively and quantitatively. Results showed that both rainfall and QGE showed increasing trends from 1996 to 2020, while the W values decreased. The correlation between QGE and W was weaker in wet years than in normal years but was the highest in dry years. The mutation time was determined to be 2004. Based on the slope-changing ratio of the cumulative quantity method and the elastic coefficient method, it was determined that the contribution of rainfall changes to W was 22.08% and that of QGE was 77.92%. This study highlights the effectiveness of the integration of qualitative analyses and quantitative evaluation for identifying the influence of external factors on groundwater and well documents that the elastic coefficient method can be used in this field. More attention should be focused on the scientific management of QGE to minimize its negative influence on the sustainable development of groundwater.

This letter proposes a perceptual metric for speech quality evaluation, which is suitable, as a loss function, for training deep learning methods. This metric, derived from the perceptual evaluation of the speech quality algorithm, is computed in a per-frame basis and from the power spectra of the reference and processed speech signal. Thus, two disturbance terms, which account for distortion once auditory masking and threshold effects are factored in, amend the mean square error (MSE) loss function by introducing perceptual criteria based on human psychoacoustics. The proposed loss function is evaluated for noisy speech enhancement with deep neural networks. Experimental results show that our metric achieves significant gains in speech quality (evaluated using an objective metric and a listening test) when compared to using MSE or other perceptual-based loss functions from the literature.

The main purpose of this article is to apply feed forward back propagation neural network (FNN) to predict groundwater level of Aghili plain, which is located in southwestern Iran. An optimal design is completed for the two hidden layers with four different algorithms: descent with momentum (GDM), Levenberg Marquardt (LM), resilient back propagation (RP), and scaled conjugate gradient (SCG). The training data for ANN is obtained from observation data. Rain, evaporation, relative humidity, temperature, discharge of irrigation canal, and groundwater recharge from the plain boundary were used in input layer while future groundwater level was used as output layer. Before training, the available data were divided into three groups, according to hydrogeological characteristics of different parts of the plain surrounding each piezometer. Statistical analysis in terms of Mean-Square-Error (MSE) and correlation coefficient (R) was used to investigate the prediction performance of ANN. FFN-LM algorithm has shown best result in the present study for all three hydrogeological groups. Now, to predict water level, the t time data (October 2003 to July 2009) and t+1 time data (October 2004 to July 2010) were used as input and output respectively. The best condition of this network was achieved for each group of data. Next, with defining the new input data related to August 2010 to January 2011 groundwater level was predicted for the following year. The achieved results of ANN model in contrast with results of finite difference model showed very high accuracy of artificial neural network in predicting groundwater level.

Accurate forecasting of groundwater level dynamics poses a critical challenge for sustainable water management in arid regions. However, the strong spatiotemporal heterogeneity inherent in groundwater systems and their complex interactions between natural processes and human activities often limit the effectiveness of conventional prediction methods. To address this, a hybrid CNN-LSTM deep learning model is constructed. This model is designed to extract multivariate coupled features and capture temporal dependencies from multi-variable time series data, while simultaneously simulating the nonlinear and delayed responses of aquifers to groundwater abstraction. Specifically, the convolutional neural network (CNN) component extracts the multivariate coupled features of hydro-meteorological driving factors, and the long short-term memory (LSTM) network component models the temporal dependencies in groundwater level fluctuations. This integrated architecture comprehensively represents the combined effects of natural recharge–discharge processes and anthropogenic pumping on the groundwater system. Utilizing monitoring data from 2021 to 2024, the model was trained and tested using a rolling time-series validation strategy. Its performance was benchmarked against traditional models, including the autoregressive integrated moving average (ARIMA) model, recurrent neural network (RNN), and standalone LSTM. The results show that the CNN-LSTM model delivers superior performance across diverse hydrogeological conditions: at the upstream well AJC-7, which is dominated by natural recharge and discharge, the Nash–Sutcliffe efficiency (NSE) coefficient reached 0.922; at the downstream well AJC-21, which is subject to intensive pumping, the model maintained a robust NSE of 0.787, significantly outperforming the benchmark models. Further sensitivity analysis reveals an asymmetric response of the model’s predictions to uncertainties in pumping data, highlighting the role of key hydrogeological processes such as delayed drainage from the vadose zone. This study not only confirms the strong applicability of the hybrid deep learning model for groundwater level prediction in data-scarce arid regions but also provides a novel analytical pathway and mechanistic insight into the nonlinear behavior of aquifer systems under significant human influence.

Objective.Functional brain network (FBN) methods are commonly integrated with deep learning (DL) models for EEG analysis. Typically, an FBN is constructed to extract features from EEG data, which are then fed into a DL model for further analysis. Beyond this two-step approach, there is potential to embed FBN construction directly within DL models as a feature extraction module, enabling the models to learn EEG representations end-to-end while incorporating insights from FBNs. However, a critical prerequisite is whether DL models can effectively learn the FBN construction process.Approach.To address this, we propose using DL models to learn FBN matrices derived from EEG data. The ability of DL models to accurately reproduce these matrices would validate their capacity to learn the FBN construction process. This approach is tested on two publicly available EEG datasets, utilizing seven DL models to learn four representative FBN matrices. Model performance is assessed through mean squared error (MSE), Pearson correlation coefficient (Corr), and concordance correlation coefficient (CCC) between predicted and actual matrices.Main results.The results show that DL models achieve low MSE and relatively high Corr and CCC values when learning the Coherence network. Visualizations of predicted and error matrices reveal that while DL models capture the general structure of all four FBNs, certain regions remain difficult to model accurately. Additionally, a pairedt-test comparing global efficiency and nodal degree between predicted and actual networks indicates that most predicted networks significantly differ from the actual networks (p<0.05).Significance.These findings suggest that while DL models can learn the connectivity relationships of certain FBNs, they struggle to capture the intrinsic topological structures. This highlights the irreplaceability of traditional FBN methods in EEG analysis and underscores the need for hybrid strategies that combine FBN methods with DL models for a more comprehensive analysis.

Distinguishing between management-induced and climatic trends in phreatic groundwater levels

Prediction of landslide movements with practical application for landslide risk mitigation is a challenge for scientists. This study presents a methodology for prediction of landslide movements using random forests, a machine learning algorithm based on regression trees. The prediction method was established based on a time series consisting of 2 years of data on landslide movement, groundwater level and precipitation gathered from the Kostanjek landslide monitoring system and nearby meteorological stations in Zagreb (Croatia). Because of complex relations between precipitations and groundwater levels, the process of landslide movement prediction is divided into two separate models: (1) model for prediction of groundwater levels from precipitation data; and (2) model for prediction of landslide movements from groundwater level data. In a groundwater level prediction model, 75 parameters were used as predictors, calculated from precipitation and evapotranspiration data. In the landslide movement prediction model, 10 parameters calculated from groundwater level data were used as predictors. Model validation was performed through the prediction of groundwater levels and prediction of landslide movements for the periods from 10 to 90 days. The validation results show the capability of the model to predict the evolution of daily displacements, from predicted variations of groundwater levels, for the period up to 30 days. Practical contributions of the developed method include the possibility of automated predictions, updated and improved on daily basis, which would be an important source of information for decisions related to crisis management in the case of risky landslide movements.