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.

翻译：推理系统动力学是许多科学研究中最重要的分析方法之一。以系统的初始状态为输入，近年来基于图神经网络（GNNs）的方法能够高精度地预测长时间跨度的未来状态。尽管这些方法在建模系统的坐标和相互作用力方面具有多样化的设计，但我们表明它们实际上共享一个通用范式，即学习速度在初始坐标和终端坐标之间区间上的积分。然而，它们的被积函数随时间恒定不变。受这一观察启发，我们提出了一种新方法，基于牛顿-柯特斯公式的若干速度估计来预测积分，并从理论上证明了其有效性。在多个基准上的大量实验经验性地表明，与最先进的方法相比，该方法具有一致且显著的改进。