Special Session 27

Machine Learning for Numerical Methods in PDEs

Organizers: Alessandro Alla (University of Rome “La Sapienza”, Italy), Alvaro Coutinho (Federal University of Rio de Janeiro, Brazil), Sandra Pieraccini (Polytechnic University of Turin, Italy)

MSC codes: 65M-XX, 68T07

Description:

In recent years, machine learning (ML) has emerged as a powerful tool for enhancing and accelerating numerical methods for partial differential equations (PDEs). Data-driven approaches are being increasingly integrated with classical numerical analysis to improve accuracy, efficiency, and generalization across complex systems. This special session aims to bring together researchers working at the interface between ML and scientific computing to discuss advances in surrogate modeling, operator learning, neural PDE solvers, and hybrid physics-informed methods. The session welcomes contributions that explore novel architectures, theoretical insights, and practical applications of MLenhanced solvers for PDEs in engineering, physics, and applied mathematics. Topics of interest include, but are not limited to, physics-informed neural networks, reduced-order modeling, data assimilation, uncertainty quantification, and adaptive discretization guided by learning algorithms. By fostering dialogue between experts in numerical analysis and machine learning, this session seeks to promote new ideas and collaborations toward the next generation of computational methods for PDEs.