Scale-PINN: Learning Efficient Physics-Informed Neural Networks Through Sequential Correction

TL;DR

Scale-PINN introduces a sequential correction strategy that significantly accelerates training and improves accuracy of physics-informed neural networks by integrating residual correction principles from numerical methods.

Contribution

It presents a novel sequential correction algorithm that enhances PINN training efficiency and accuracy by embedding iterative residual correction into the loss function.

Findings

Reduces training time from hours to under 2 minutes on fluid dynamics problems.

Achieves superior accuracy compared to existing PINNs.

Enables application to complex problems in aerodynamics and urban science.

Abstract

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern numerical solvers. We introduce the Sequential Correction Algorithm for Learning Efficient PINN (Scale-PINN), a learning strategy that bridges modern physics-informed learning with numerical algorithms. Scale-PINN incorporates the iterative residual-correction principle, a cornerstone of numerical solvers, directly into the loss formulation, marking a paradigm shift in how PINN losses can be conceived and constructed. This integration enables Scale-PINN to achieve unprecedented convergence speed across PDE problems from different physics domain, including reducing training time on a challenging fluid-dynamics problem for state-of-the-art PINN from hours to sub-2 minutes while maintaining superior accuracy, and enabling application to representative problems in aerodynamics and urban science. By uniting the rigor of numerical methods with the flexibility of deep learning, Scale-PINN marks a significant leap toward the practical adoption of PINNs in science and engineering through scalable, physics-informed learning. Codes are available at https://github.com/chiuph/SCALE-PINN.