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.

提出了一种具有模块化和物理归纳偏差的结构神经网络框架，即 Modular Lagrangian Network (ModLaNet)，它利用模块化来建模每个元素的能量，并通过拉格朗日力学构建目标动力学系统，从而可以从简单系统的动力学中学习并扩展到更复杂的系统，以提高其他相关物理感知神经网络不具备的数据效率和准确性性能。在对双摆和三体系统进行建模的同时，还将模型重新组织为扩展模型，用于模拟多摆和多体系统，展示了该框架的有趣的可重用性特征。