Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics
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 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.
Cite
@article{arxiv.2402.10680,
title = {Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics},
author = {Anas Jnini and Flavio Vella and Marius Zeinhofer},
journal= {arXiv preprint arXiv:2402.10680},
year = {2024}
}