Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systems
This work addresses the challenge of accurately modeling time evolution in dynamic systems for scientific studies, representing an incremental advancement over existing GNN-based methods.
The paper tackles the problem of predicting future states in dynamic systems using graph neural networks (GNNs) by proposing a new approach based on Newton-Cotes formulas to improve velocity integration, resulting in consistent and significant improvements over state-of-the-art methods in experiments.
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.