通过投影方法强制物理守恒律，显著提升PINN的准确性与稳定性。
Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks
- 引入投影机制，确保神经网络输出满足守恒定律
- 动量守恒误差降低三到四个数量级，预测误差大幅下降
- 适合需要严格物理一致性建模的科学计算场景
物理信息神经网络（PINNs）将物理定律融入训练过程，以极少数据高效求解偏微分方程（PDEs）。然而，传统PINNs无法保证守恒律的满足，而守恒律在物理系统建模中同样关键。为此，本文提出PINN-Proj，一种基于投影的新方法，用于强制实施守恒律。实验表明，PINN-Proj在动量守恒方面显著优于标准PINN，预测误差比最佳基准降低三至四个数量级；在三个PDE数据集上的状态预测任务中也表现略优。
原文摘要 · Abstract (English)
Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are also important to consider in modeling physical systems. To address this, we proposed PINN-Proj, a PINN-based model that uses a novel projection method to enforce conservation laws. We found that PINN-Proj substantially outperformed PINN in conserving momentum and lowered prediction error by three to four orders of magnitude from the best benchmark tested. PINN-Proj also performed marginally better in the separate task of state prediction on three PDE datasets.
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