Spatiotemporal Compositional Active Sampling for Physics-Informed Neural Networks

Abstract

Physics-informed neural networks (PINNs) approximate partial differential equations (PDEs) by enforcing governing equations and boundary conditions during training, but their accuracy depends on how collocation points are distributed and updated. We propose spatiotemporal compositional active sampling (STCAS), a reference-assisted offline configuration procedure that uses an analytic or high-accuracy numerical solution to rank complete three-stage sampling plans. It screens eight fixed rules, forms a task-specific shortlist, and evaluates bounded fixed, switched, and locally blended plans with independent selection sets and a composition guard. A safety-anchor decision retains the standard PINN unless the selected candidate is at least 5% better. Across five evaluations on 18 analytically specified two-dimensional Poisson tasks, this protocol improves 16 task means and ties two, reducing aggregate relative-L2 error by 12.8% (hierarchical-bootstrap 95% interval [6.78%,19.32%]; one-sided paired Wilcoxon p=2.19×10−4). Against the confirmed fixed plan, aggregate error decreases by 8.2%. In comparison experiments designed for two transfer tasks and matched for main PINN training budgets, STCAS achieves the lowest aggregate mean reported error among the compared methods for both a steady convection–diffusion equation and a nonlinear time-dependent Burgers equation; its offline search cost is additional.