ETNA: Efficient Time-Stepping Numerical Approaches for PDEs - Forward and Inverse Models with Applications

This workshop explores recent advances in the development and analysis of time-stepping methods for forward and inverse models governed by partial differential equations (PDEs), with a dual focus on geophysical applications and numerical methodology. The workshop aims at disseminating the results of the PRIN PNRR project “FIN4GEO: Forward and Inverse Numerical modeling of hydrotermal systems in volcanic regions with application to GEOtermal energy exploitation”, as well as foster collaboration with researchers beyond the project, including experts in geophysics, numerical analysis, and scientific machine learning. On the application side, we focus on dynamic geophysical systems such as subsurface fluid flow, hydrothermal circulation, volcanic and seismic processes, and the interpretation of geophysical observables. These phenomena involve multiscale, multiphysics interactions in evolving domains, posing significant challenges for modeling and simulation. On the numerical side, we highlight innovations in time integration techniques, high-order conservative schemes for hyperbolic systems, and robust algorithms for fluid-structure interaction and moving interfaces. The workshop will also feature recent advances in scientific machine learning approaches for PDEs, including physics-informed neural networks (PINNs) and hybrid methods that integrate linearization, model order reduction, and low-rank manifold approximations to improve the efficiency and reliability of inverse modeling. These techniques are particularly relevant to the estimation of hydrothermal parameters from noisy geophysical observations, where combining physics-based models with data-driven learning yields improved accuracy and interpretability. Beyond geophysics, the workshop includes contributions that advance numerical methods for PDEs more broadly, including applications in optimal control, social dynamics, and simulation of complex flows in multiphysics environments. We aim to bring together geophysicists, numerical analysts, and scientific machine learning researchers to promote cross-disciplinary discussion, share cutting-edge techniques, and encourage collaboration across modelling, numerical methods and real-world applications.