Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems

TL;DR

This paper introduces parameterized neural ODEs (PNODEs) that incorporate input parameters to learn multiple dynamics, enabling efficient modeling of complex physical systems for rapid simulations.

Contribution

The paper extends neural ODEs by adding input parameters, allowing learning of multiple dynamics, and applies this to computational physics for faster simulation of complex processes.

Findings

PNODEs effectively model multiple physical dynamics.

Demonstrated success on computational physics benchmarks.

Enables rapid, parameter-dependent simulations.

Abstract

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ordinary differential equations, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder-decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs with important benchmark problems from computational physics.