Weak Form Generalized Hamiltonian Learning

TL;DR

This paper introduces a novel method for learning generalized Hamiltonian decompositions from noisy data, enabling physics-informed modeling of dynamical systems with reduced computational cost.

Contribution

It presents a new weak form approach for learning continuous-time models that unifies previous physics-inspired deep learning methods and is computationally efficient.

Findings

Successfully learns energy functions from noisy data

Unifies and extends previous physics-informed modeling approaches

Reduces computational complexity compared to adjoint methods

Abstract

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.