A Physics-Informed Error Field Learning (PIEFL) framework for PINNs is proposed, which avoids continuous optimization of the entire solution space and focuses computational resources on correcting existing prediction errors.
Abstract
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 achieves satisfactory accuracy and shifts the learning objective from the solution field to the error field. By deriving error control equations under physical constraints, the error network learns the discrepancy between the current approximation and the exact solution, and the learned error correction is combined with the primary prediction to improve solution accuracy. The proposed framework avoids continuous optimization of the entire solution space and focuses computational resources on correcting existing prediction errors. Moreover, PIEFL requires no modification to the primary network architecture, making it compatible with existing PINN models and applicable as a general post-training optimization strategy. Numerical experiments on representative PDEs demonstrate that PIEFL achieves higher solution accuracy under the same computational budget, validating its effectiveness in improving the performance of PINNs.
This work proposes a novel physics-informed broad learning system (PI-BLS), the first physics-informed learning framework based on broad RdNNs that achieves competitive and often superior performance with reduced training time and model parameters compared with conventional PINNs.
Pinki Khatun, M. Sajid, Abhinav Jha et al.· arXiv.org· 0 citations
The results demonstrate that PINN achieves more accurate and stable full-field vibration reconstructions than conventional PINNs, particularly under conditions involving high-frequency modes, and highlights the potential of hybrid data-physics neural frameworks as an efficient and reliable approach for solving complex PDE-governed dynamical systems.
Hai-Long Liu, S. Hedayatrasa, Yunpeng Zhu et al.· e-Journal of Nondestructive...· 0 citations
This review synthesizes recent advances in loss function designs for Physics-Informed Neural Networks (PINNs), a transformative approach to solving partial differential equations (PDEs) by embedding physical laws into deep learning frameworks, to equip researchers with insights to refine PINN methodologies.
M. Esmaeilbeigi, Daniela Annunziata, Salvatore Cuomo et al.· Journal of Scientific Comput...· 0 citations
A continual-learning physics-informed neural network (CL-PINN), which combines Bayesian-optimization-based active parameter selection, task-wise dynamic loss weighting, sparse physics-constrained replay, and an optional parameter subnetwork to improve task allocation and knowledge retention under bounded active-task capacity.
Xujia Chen, Xinyu Hu, Letian Chen et al.· 0 citations
Black-box optimization of expensive functions governed by physical laws remains challenging for standard Gaussian process (GP)-based Bayesian optimization (BO), which can become computationally demanding and does not naturally embed physical constraints. Existing physics-informed neural network (PINN)-based Bayesian optimization methods, hereafter termed PINN-BO methods, lack predictive uncertainty for guiding exploration, rely on fixed loss weights, and employ inefficient single-point sampling. We propose adaptive loss-weighted Bayesian optimization (AL-BO), an uncertainty-aware BO framework with a PINN surrogate that addresses all three limitations. Monte Carlo dropout (MC dropout) is incorporated to estimate epistemic uncertainty and guide acquisition. GradNorm-based adaptive loss weighting dynamically balances data fidelity and physics constraint losses during training. A lower-confidence-bound (LCB) batch acquisition strategy replaces single-point sampling to accelerate convergence. The convergence behavior and applicability of the proposed framework are discussed under the calibrated uncertainty estimates. Experiments on selected synthetic benchmarks and two chemical engineering case studies demonstrate that AL-BO achieves better optimization performance than comparable GP-BO and neural network-based baselines under the same function-evaluation budget.
Zhi-Qin Kuang, Jingyi Lu· Industrial & Engineering...· 0 citations
The proposed ARH-PINNs can accurately resolve large-gradient fields such as shock waves, while effectively suppressing non-physical oscillations and retaining low numerical dissipation.
Ting-Jie Li, Su-Pei Zheng, Feng Hu et al.· The Physics of Fluids· 1 citation
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
