Weak Form Generalized Hamiltonian Learning

Understand

We present a method for learning generalized Hamiltonian decompositions of ordinary differential equations given a set of noisy time series measurements.

• Our method simultaneously learns a continuous time model and a scalar energy function for a general dynamical system.
• Learning predictive models in this form allows one to place strong, high-level, physics inspired priors onto the form of the learnt governing equations for general dynamical systems.
• Moreover, having shown how our method extends and unifies some previous work in deep learning with physics inspired priors, we present a novel method for learning continuous time models from the weak form of the governing equations which is less computationally taxing than standard adjoint methods.