Shuo Zhang

Training neural operators needs expensive numerical solution labels, while PDE inputs and governing equations are cheap physical information. PI-Init spends that information on initialization: it pretrains on unlabeled inputs with physics losses, then keeps the parameters for supervised fine-tuning. At matched label budgets, FNO prediction error falls 53.3% on Burgers and 62.7% on 1D Advection, and on Burgers 200 labeled trajectories beat supervised-only training with 2,000.

Training neural operators needs expensive numerical solution labels, while PDE inputs and governing equations are cheap physical information. PI-Init spends that information on initialization: it pretrains on unlabeled inputs with physics losses, then keeps the parameters for supervised fine-tuning. At matched label budgets, FNO prediction error falls 53.3% on Burgers and 62.7% on 1D Advection, and on Burgers 200 labeled trajectories beat supervised-only training with 2,000.