arXiv subjects

Abdourrahmane M. Atto

Publications and source records attributed to Abdourrahmane M. Atto.

3 recordsLinked to original sources

arXiv2026

Pure and physics-guided deep learning approaches for spatio-temporal groundwater level prediction

Groundwater represents a key element of the water cycle, yet it exhibits complex and context-dependent relationships that make its modeling challenging. Theory-based models have been the cornerstone of scientific understanding. However, their computational cost, simplifying assumptions, and calibration requirements limit their use. In recent years, data-driven models have emerged as powerful alternatives. In particular, deep learning has proven to be a promising approach for its design flexibility and ability to learn complex relationships directly from the data without requiring extensive domain information. We proposed an attention-based pure deep learning model, named STAINet, to predict weekly groundwater levels in Piedmont (Italy), leveraging both irregular groundwater time series and weather image sequences. To enhance the model's trustworthiness and generalization ability, we merged the theory and data-driven approaches by considering physics-guided strategies to inject the groundwater flow equation into the model. Firstly, we restructured the tail of the architecture to predict the three terms of the governing equation, named the autoregressive, diffusion, and residual components - we thus obtained the PSTAINet-IB. Then, we further injected physics priors by adding loss terms related to the estimated equation components, obtaining the PSTAINet-ILB model. Lastly, we developed the PSTAINet-ILRB by imposing a loss term specific to the residual component, which forces the groundwater recharge to occur within the groundwater body recharge zone, which is identified by domain experts. The models were evaluated both by feeding true lagged values as input and by iterating their own predictions (rollouts) over the whole test set. The PSTAINet-ILB model performed the best, achieving remarkable test performance, and generating equation components in line with domain experts' expectations.

cs.LG↗

arXiv2026

Smooth SCAD: A Raised Cosine SCAD Type Thresholding Rule for Wavelet Denoising

We introduce a smooth variant of the SCAD thresholding rule for wavelet denoising by replacing its piecewise linear transition with a raised cosine. The resulting shrinkage function is odd, continuous on R, and continuously differentiable away from the main threshold, yet retains the hallmark SCAD properties of sparsity for small coefficients and near unbiasedness for large ones. This smoothness places the rule within the continuous thresholding class for which Stein's unbiased risk estimate is valid. As a result, unbiased risk computation, stable data-driven threshold selection, and the asymptotic theory of Kudryavtsev and Shestakov apply. A corresponding nonconvex prior is obtained whose posterior mode coincides with the estimator, yielding a transparent Bayesian interpretation. We give an explicit SURE risk expression, discuss the oracle scale of the optimal threshold, and describe both global and level-dependent adaptive versions. The smooth SCAD rule therefore offers a tractable refinement of SCAD, combining low bias, exact sparsity, and analytical convenience in a single wavelet shrinkage procedure.

stat.CO↗

arXiv2025

Time Distributed Deep Learning Models for Purely Exogenous Forecasting: Application to Water Table Depth Prediction using Weather Image Time Series

Groundwater resources are one of the most relevant elements in the water cycle, therefore developing models to accurately predict them is a pivotal task in the sustainable resource management framework. Deep Learning (DL) models have been revealed to be very effective in hydrology, especially by feeding spatially distributed data (e.g. raster data). In many regions, hydrological measurements are difficult to obtain regularly or periodically in time, and in some cases, the last available data are not up to date. Reversely, weather data, which significantly impacts water resources, are usually more available and with higher quality. More specifically, we have proposed two different DL models to predict the water table depth in the Grana-Maira catchment (Piemonte, IT) using only exogenous weather image time series. To deal with the image time series, both models are made of a first Time Distributed Convolutional Neural Network (TDC) which encodes the image available at each time step into a vectorial representation. The first model, TDC-LSTM uses then a Sequential Module based on an LSTM layer to learn temporal relations and output the predictions. The second model, TDC-UnPWaveNet uses instead a new version of the WaveNet architecture, adapted here to output a sequence shorter and completely shifted in the future with respect to the input one. To this aim, and to deal with the different sequence lengths in the UnPWaveNet, we have designed a new Channel Distributed layer, that acts like a Time Distributed one but on the channel dimension, i.e. applying the same set of operations to each channel of the input. TDC-LSTM and TDC-UnPWaveNet have shown both remarkable results. However, the two models have focused on different learnable information: TDC-LSTM has focused more on lowering the bias, while TDC-UnPWaveNet has focused more on the temporal dynamics, maximizing correlation, and KGE.

cs.LG↗