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，近期基于图神经网络（GNNs）的方法能够高精度地预测未来长时间的状态。尽管这些方法在建模系统的坐标和相互作用力时具有多样的设计，我们证明它们实际上共享一个通用范式，即学习速度在初始坐标与终端坐标之间的积分。然而，它们的被积函数关于时间是恒定的。受此观察启发，我们提出了一种基于牛顿-科特斯公式的多个速度估计来预测积分的新方法，并从理论上证明了其有效性。在多个基准上的广泛实验实证表明，与最前沿的方法相比，该方法具有一致且显著的改进。