Physics-Informed Error Field Learning Boosts PINN Accuracy Post-Training.

Physics-Informed Neural Networks (PINNs) are powerful tools for solving partial differential equations, but their accuracy improvements often diminish in later optimization stages, leading to increased computational costs. A new framework, Physics-Informed Error Field Learning (PIEFL), addresses this by shifting the learning objective. Instead of continuously optimizing the main network, PIEFL introduces a secondary "error network" once the primary PINN reaches a good level of accuracy. This error network is specifically trained to identify and correct the discrepancies between the primary network's predictions and the true solution, guided by physical constraints. This approach allows computational resources to be focused on refining existing errors rather than re-optimizing the entire solution space. PIEFL is designed to be compatible with existing PINN architectures, acting as a general post-training enhancement. Experiments show it significantly improves solution accuracy for various PDEs within the same computational budget.