Learning iterative algorithms to solve PDEs.

Lise Le Boudec, Emmanuel de Bezenac, Louis Serrano, Yuan Yin, patrick gallinari

Keywords: PDE, Solver, Physics-Informed

TL;DR: This paper proposes an optimized solver for PDEs, based on physics informed losses.

Abstract: In this work, we propose a new method to solve partial differential equations (PDEs). Taking inspiration from traditional numerical methods, we view approx- imating solutions to PDEs as an iterative algorithm, and propose to learn the it- erations from data. With respect to directly predicting the solution with a neural network, our approach has access to the PDE, having the potential to enhance the model’s ability to generalize across a variety of scenarios, such as differing PDE parameters, initial or boundary conditions. We instantiate this framework and empirically validate its effectiveness across several PDE-solving benchmarks, evaluating efficiency and generalization capabilities, and demonstrating its poten- tial for broader applicability.

Submission Number: 69