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Deep learning models are able to approximate one specific dynamical systembut struggle at learning generalisable dynamics, where dynamical systems obeythe same laws of physics but contain different numbers of elements (e.g.,double- and triple-pendulum systems). To relieve this issue, we proposed theModular Lagrangian Network (ModLaNet), a structural neural network frameworkwith modularity and physical inductive bias. This framework models the energyof each element using modularity and then construct the target dynamical systemvia Lagrangian mechanics. Modularity is beneficial for reusing trained networksand reducing the scale of networks and datasets. As a result, our framework canlearn from the dynamics of simpler systems and extend to more complex ones,which is not feasible using other relevant physics-informed neural networks. Weexamine our framework for modelling double-pendulum or three-body systems withsmall training datasets, where our models achieve the best data efficiency andaccuracy performance compared with counterparts. We also reorganise our modelsas extensions to model multi-pendulum and multi-body systems, demonstrating theintriguing reusable feature of our framework.

ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias