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

• URL: http://arxiv.org/abs/2305.14642v3
• Date: Fri, 20 Oct 2023 01:32:45 GMT
• Title: Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systems
• Authors: Lingbing Guo, Weiqing Wang, Zhuo Chen, Ningyu Zhang, Zequn Sun, Yixuan Lai, Qiang Zhang, and Huajun Chen
• Abstract summary: We propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas. Experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.
• Score: 49.50674348130157
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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