用傅里叶分解与随机边界条件训练，让PINN能泛化预测任意边界下的解。
Plane-Wave Decomposition and Randomised Training; a Novel Path to Generalised PINNs for SHM
- 基于傅里叶分解学习解的形式，结合随机边界条件训练。
- 训练后可预测任意边界条件下的解，且在样本间实现精准插值。
- 适合需要快速泛化预测的结构健康监测场景。
本文提出一种基于傅里叶分解形式学习与随机边界条件训练的物理信息神经网络（PINN）新方法。通过该方法训练的PINN具备泛化能力：训练完成后可准确预测任意边界条件下的解，并在训练样本覆盖的区间内实现解的精确插值。以两个耦合振子的简化系统为例，验证了该方法能有效降低训练与推理时间比，使模型具备真正的预测能力，核心在于将解的求解过程从特定边界条件中解耦。
原文摘要 · Abstract (English)
In this paper, we introduce a formulation of Physics-Informed Neural Networks (PINNs), based on learning the form of the Fourier decomposition, and a training methodology based on a spread of randomly chosen boundary conditions. By training in this way we produce a PINN that generalises; after training it can be used to correctly predict the solution for an arbitrary set of boundary conditions and interpolate this solution between the samples that spanned the training domain. We demonstrate for a toy system of two coupled oscillators that this gives the PINN formulation genuine predictive capability owing to an effective reduction of the training to evaluation times ratio due to this decoupling of the solution from specific boundary conditions.
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