Si chiude, con l'appuntamento di mercoledì 7 giugno alle 14. 30 il ciclo 2023 dei Seminari AIM.
Ospite della giornata è Salvatore Cuomo, professore di analisi numerica del Dipartimento di Matematica e Applicazioni "Renato Caccioppoli" dell'Università Federico II di Napoli.
Il titolo del talk è: The novel Scientific Machine Learning paradigm for solving the Groundwater Flow Equation.
Di seguito l'abstract.
"In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained wide popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning frameworks for solving forward and inverse problems with non-linear PDEs. Recently, PINNs have shown promising results in different application domains. In this paper, we approach the groundwater flow equations numerically by searching for the unknown hydraulic head. Since singular terms in differential equations are very challenging from a numerical point of view, we approximate the Dirac distribution by different regularization terms. Furthermore, from a computational point of view, this study investigates how a PINN can solve higher-dimensional flow equations. In particular, we analyze the approximation error for one and two-dimensional cases in a statistical learning framework. The numerical experiments discussed include one and two-dimensional cases of a single or multiple pumping well in an infinite aquifer, demonstrating the effectiveness of this approach in the hydrology application domain.”.
Il seminario sarà trasmesso in streaming sul canale YouTube CNR IAC.
Qui il programma completo dei seminari.