Noisy PDE Training Requires Bigger PINNs

ArXi:2507.06967v2 Announce Type: replace Physics-Informed Neural Networks (PINNs) are increasingly used to approximate solutions of partial differential equations (PDEs), particularly in high dimensions. In real-world settings, data are often noisy, making it crucial to understand when a predictor can still achieve low empirical risk. Yet, little is known about the conditions under which a PINN can do so effectively.