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Physics-Informed Error Field Learning: A Post-Training Optimization Framework for Physics-Informed Neural Networks

arXiv · AI, language, vision and robotics · article · Aug 25, 2026 · UTC

Physics-Informed Neural Networks (PINNs) have emerged as an important class of numerical methods for solving partial differential equations (PDEs). However, during the late-stage optimization process, further parameter updates often yield diminishing accuracy improvements while increasing computational costs. To address this issue, this paper proposes a Physics-Informed Error Field Learning (PIEFL) framework for PINNs. Unlike conventional approaches that continuously approximate the solution field using a single network, PIEFL introduces an auxiliary error network after the primary network ach

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