• Introduces a flow-aware training strategy for PINNs based on the information flow in the domain. • Decomposes the domain into geodesic subdomains that are progressively supervised via an epoch-based schedule. • Matches or improves baseline accuracy while reducing computational costs across seven PDE benchmarks. • Prevents uninformative updates and misleading gradients in regions where the solution is not yet determined. Physics-Informed Neural Networks (PINNs) typically update parameters at all collocation points from the first epoch, even in regions still unreachable from boundary or initial conditions. In these zones, early updates may be uninformative or harmful, as residual gradients often correlate poorly with the true error. We introduce a flow-aware training strategy that delays supervision until the governing physics can propagate meaningful information. The computational mesh is decomposed into geodesic subdomains ranked by distance from an information boundary, where initial or boundary conditions are applied, and progressively activated according to an epoch schedule. This selective exposure concentrates optimization where updates are most effective, preventing wasted capacity and misleading gradients in causally disconnected regions. The method requires no architectural changes and uses the standard PINN loss; only the sampling mask evolves over time. Benchmarks on seven PDE problems show that flow-aware training matches or improves baseline accuracy while reducing computational cost.
Cestola et al. (Tue,) studied this question.