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