Learning nonlinear invariant manifolds with structure-aware neural networks

We present a structured approach to learning nonlinear dynamical systems with neural networks. Standard neural networks, while expressive, often fail to identify the underlying physics of the system, producing inaccurate emulators even within the domain of training. In response, our proposed model draws inspiration from the Shaw–Pierre construction of nonlinear normal modes, by encoding inductive bias to constrain learning to invariant manifolds in phase space, which decouple nonlinear oscillators. The physics-informed architecture and loss functions are evaluated on autonomous oscillatory systems to demonstrate that the learned neural network is interpretable, approximating the nonlinear modal subspace, to which the learned dynamics are confined. The construction produces a structure-aware neural network for nonlinear dynamical systems, with faster training and better generalisation when compared to conventional black-box architectures.

Venue: Fulton G20