Learning in Sinusoidal Spaces with Physics-Informed Neural Networks

Understand

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.

• However, it turns out to be difficult to train an accurate PINN model for many problems in practice.
• In this paper, we present a novel perspective of the merits of learning in sinusoidal spaces with PINNs.
• By analyzing behavior at model initialization, we first show that a PINN of increasing expressiveness induces an initial bias around flat output functions.