Abdourrahmane M. Atto

Matteo Salis, Gabriele Sartor, Rosa Meo et al.

Groundwater represents a key element of the water cycle, yet it exhibits intricate and context-dependent relationships that make its modeling a challenging task. Theory-based models have been the cornerstone of scientific understanding. However, their computational demands, 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 leading approach for its design flexibility and ability to learn complex relationships. We proposed an attention-based pure deep learning model, named STAINet, to predict weekly groundwater levels at an arbitrary and variable number of locations, leveraging both spatially sparse groundwater measurements and spatially dense weather information. Then, to enhance the model's trustworthiness and generalization ability, we considered different physics-guided strategies to inject the groundwater flow equation into the model. Firstly, in the STAINet-IB, by introducing an inductive bias, we also estimated the governing equation components. Then, by adopting a learning bias strategy, we proposed the STAINet-ILB, trained with additional loss terms adding supervision on the estimated equation components. Lastly, we developed the STAINet-ILRB, leveraging the groundwater body recharge zone information estimated by domain experts. The STAINet-ILB performed the best, achieving overwhelming test performances in a rollout setting (median MAPE 0.16%, KGE 0.58). Furthermore, it predicted sensible equation components, providing insights into the model's physical soundness. Physics-guided approaches represent a promising opportunity to enhance both the generalization ability and the trustworthiness, thereby paving the way to a new generation of disruptive hybrid deep learning Earth system models.

Matteo Salis, Abdourrahmane M. Atto, Stefano Ferraris et al.

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.

Abdourrahmane Mahamane Atto

The paper proposes a 4-step process for highlighting that softlog-softmax cascades can improve both consistency and dependability of the next generation ensemble learning systems. The first process is anatomical in nature: the target ensemble model under consideration is composed by canonical elements relating to the definition of a convolutional frustum. No a priori is considered in the choice of canonical forms. Diversity is the main criterion for selecting these forms. It is shown that the more complex the problem, the more useful this ensemble diversity is. The second process is physiological and relates to neural engineering: a softlog is derived to both make weak logarithmic operations consistent and lead, through multiple softlog-softmax layers, to intermediate decisions in the sense of respecting the same class logic as that faced by the output layer. The third process concerns neural information theory: softlog-based entropy and divergence are proposed for the sake of constructing information measures yielding consistent values on closed intervals. These information measures are used to determine the relationships between individual and sub-community decisions in frustum diversitybased ensemble learning. The concluding process addresses the derivation of an informative performance tensor for the purpose of a reliable ensemble evaluation.

Hermann Courteille, A. Benoît, N Méger et al.

Deep Neural Networks (DNNs) are getting increasing attention to deal with Land Cover Classification (LCC) relying on Satellite Image Time Series (SITS). Though high performances can be achieved, the rationale of a prediction yielded by a DNN often remains unclear. An architecture expressing predictions with respect to input channels is thus proposed in this paper. It relies on convolutional layers and an attention mechanism weighting the importance of each channel in the final classification decision. The correlation between channels is taken into account to set up shared kernels and lower model complexity. Experiments based on a Sentinel-2 SITS show promising results.

Abdourrahmane Mahamane Atto, Sylvie Galichet, Dominique Pastor et al.

The paper proposes representation functionals in a dual paradigm where learning jointly concerns both linear convolutional weights and parametric forms of nonlinear activation functions. The nonlinear forms proposed for performing the functional representation are associated with a new class of parametric neural transfer functions called rectified power sigmoid units. This class is constructed to integrate both advantages of sigmoid and rectified linear unit functions, in addition with rejecting the drawbacks of these functions. Moreover, the analytic form of this new neural class involves scale, shift and shape parameters so as to obtain a wide range of activation shapes, including the standard rectified linear unit as a limit case. Parameters of this neural transfer class are considered as learnable for the sake of discovering the complex shapes that can contribute in solving machine learning issues. Performance achieved by the joint learning of convolutional and rectified power sigmoid learnable parameters are shown outstanding in both shallow and deep learning frameworks. This class opens new prospects with respect to machine learning in the sense that learnable parameters are not only attached to linear transformations, but also to suitable nonlinear operators.