Work

Gauss-Newton Natural Gradient Descent for Physics-informed Computational Fluid Dynamics

Year: 2025

Type: article

Abstract: We propose Gauss-Newton’s method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the function space dynamics. Our computational results demonstrate close to single-precision accuracy measured in relative L 2 norm on a number of benchmark problems. To the best of our knowledge, this constitutes the first contribution in the PINN literature that solves the Navier-Stokes equations to this degree of accuracy. Finally, we show that given a suitable integral discretization, the proposed optimization algorithm agrees with Gauss-Newton’s method in parameter space. This allows a matrix-free formulation enabling efficient scalability to large network sizes.

Source: Computers & Fluids

DOI: 10.1016/j.compfluid.2025.106955

Authors: Anas Jnini, Flavio Vella, Marius Zeinhofer

Institutions: University of Trento, ETH Zurich

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,700

Funders: Eidgenössische Technische Hochschule Zürich, Finmeccanica Group, Università degli Studi di Trento