Weak Form Generalized Hamiltonian Learning
This work provides a more efficient method for learning physics-constrained models of dynamical systems, which could benefit researchers in computational physics and machine learning.
The authors tackled the problem of learning generalized Hamiltonian decompositions from noisy time-series data, developing a method that simultaneously learns continuous-time models and scalar energy functions while incorporating physics-inspired priors. They introduced a novel weak-form approach that reduces computational costs compared to standard adjoint methods.
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.