Learning Modular Simulations for Homogeneous Systems

Jayesh K Gupta, Sai Vemprala, Ashish Kapoor

Keywords: Neural differential equations, Dynamics, Graph networks

TL;DR: We present a modular approach to model the dynamics of homogeneous networks, where the nodes are modeled using a 'message passing neural ODE' algorithm, an extension over neural ODE that enables node-node communication.

Abstract: Complex systems are often decomposed into modular subsystems for engineering tractability. Although various equation based white-box modeling techniques make use of such structure, learning based methods have yet to incorporate these ideas broadly. We present a modular simulation framework for modeling homogeneous multibody dynamical systems, which combines ideas from graph neural networks and neural differential equations. We learn to model the individual dynamical subsystem as a neural ODE module. Full simulation of the composite system is orchestrated via spatio-temporal message passing between these modules. An arbitrary number of modules can be combined to simulate systems of a wide variety of coupling topologies. We evaluate our framework on a variety of systems and show that message passing allows coordination between multiple modules over time for accurate predictions and in certain cases, enables zero-shot generalization to new system configurations. Furthermore, we show that our models can be transferred to new system configurations with lower data requirement and training effort, compared to those trained from scratch.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2210.16294/code)