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Reasoning system dynamics is one of the most important analytical approachesfor many scientific studies. With the initial state of a system as input, therecent graph neural networks (GNNs)-based methods are capable of predicting thefuture state distant in time with high accuracy. Although these methods havediverse designs in modeling the coordinates and interacting forces of thesystem, we show that they actually share a common paradigm that learns theintegration of the velocity over the interval between the initial and terminalcoordinates. However, their integrand is constant w.r.t. time. Inspired by thisobservation, we propose a new approach to predict the integration based onseveral velocity estimations with Newton-Cotes formulas and prove itseffectiveness theoretically. Extensive experiments on several benchmarksempirically demonstrate consistent and significant improvement compared withthe state-of-the-art methods.

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