Forecasting Hamiltonian dynamics without canonical coordinates
This work addresses a bottleneck for researchers and practitioners in physics and machine learning by enabling more efficient learning of energy-conserving dynamical systems from accessible data.
The paper tackled the problem of forecasting Hamiltonian dynamics without requiring canonical coordinates, which are often hard to infer from data, by introducing a method to train Hamiltonian neural networks using any set of generalized coordinates, including easily observable ones.
Conventional neural networks are universal function approximators, but because they are unaware of underlying symmetries or physical laws, they may need impractically many training data to approximate nonlinear dynamics. Recently introduced Hamiltonian neural networks can efficiently learn and forecast dynamical systems that conserve energy, but they require special inputs called canonical coordinates, which may be hard to infer from data. Here we significantly expand the scope of such networks by demonstrating a simple way to train them with any set of generalised coordinates, including easily observable ones.