Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systems

TL;DR

This paper introduces a novel graph neural network approach using Newton-Cotes formulas to better predict the time evolution of dynamic systems, improving accuracy over existing methods.

Contribution

It proposes a new GNN framework that models integration of velocity using Newton-Cotes formulas, addressing limitations of constant integrand assumptions in prior methods.

Findings

Significant accuracy improvements over state-of-the-art methods

Theoretical proof of the effectiveness of Newton-Cotes-based integration

Consistent performance gains across multiple benchmarks

Abstract

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.