Plane-Wave Decomposition and Randomised Training; a Novel Path to Generalised PINNs for SHM
This work addresses the challenge of generalizing PINNs for structural health monitoring (SHM) by enabling predictive capability across diverse boundary conditions, though it is incremental as it builds on existing PINN methods.
The paper tackles the problem of making Physics-Informed Neural Networks (PINNs) generalizable by introducing a formulation based on Fourier decomposition and randomized training with varied boundary conditions, resulting in a PINN that can predict solutions for arbitrary boundary conditions and interpolate between training samples, as demonstrated on a toy system of two coupled oscillators with an effective reduction in training-to-evaluation time ratio.
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.