2 papers
math.NA2024
Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning
Tim De Ryck, Siddhartha Mishra
Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems f…
cs.LG2023
An operator preconditioning perspective on training in physics-informed machine learning
Tim De Ryck, Florent Bonnet, Siddhartha Mishra +1
In this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize residuals connected to partial dif…