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Physical systems are commonly represented as a combination of particles, theindividual dynamics of which govern the system dynamics. However, traditionalapproaches require the knowledge of several abstract quantities such as theenergy or force to infer the dynamics of these particles. Here, we present aframework, namely, Lagrangian graph neural network (LGnn), that provides astrong inductive bias to learn the Lagrangian of a particle-based systemdirectly from the trajectory. We test our approach on challenging systems withconstraints and drag -- LGnn outperforms baselines such as feed-forwardLagrangian neural network (Lnn) with improved performance. We also show thezero-shot generalizability of the system by simulating systems two orders ofmagnitude larger than the trained one and also hybrid systems that are unseenby the model, a unique feature. The graph architecture of LGnn significantlysimplifies the learning in comparison to Lnn with ~25 times better performanceon ~20 times smaller amounts of data. Finally, we show the interpretability ofLGnn, which directly provides physical insights on drag and constraint forceslearned by the model. LGnn can thus provide a fillip toward understanding thedynamics of physical systems purely from observable quantities.

Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networks