Plane-Wave Decomposition and Randomised Training; a Novel Path to Generalised PINNs for SHM
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Abstract (arXiv)
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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References · 8
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2014Image Super-Resolution Using Deep Convolutional Networkscited by 1,224
- 2017Visualizing the Loss Landscape of Neural Netscited by 1,130
- 2014The Loss Surfaces of Multilayer Networkscited by 280
- 2021The Principles of Deep Learning Theorycited by 173
- 2018Deep Learning of Vortex Induced Vibrationscited by 76
- 2022Physical Activation Functions (PAFs): An Approach for More Efficient Induction of Physics into Physics-Informed Neural Networks (PINNs)cited by 10
- 2024Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equationscited by 4
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