论文标题
ModLanets:通过模块化和物理电感偏差学习可通用的动力学
ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias
论文作者
论文摘要
深度学习模型能够近似一个特定的动力学系统,但在学习通用动力学方面挣扎,在该动态系统中,动态系统遵守了相同的物理定律,但包含不同数量的元素(例如,双重和三铅系统)。为了缓解这个问题,我们提出了模块化拉格朗日网络(ModLanet),这是一个具有模块化和物理诱导偏置的结构神经网络框架。该框架使用模块化对每个元素的能量进行建模,然后通过拉格朗日力学构建目标动力学系统。模块化有益于重复训练的网络并减少网络和数据集的规模。结果,我们的框架可以从更简单的系统的动力学中学习,并扩展到更复杂的框架,使用其他相关的物理知识的神经网络是不可行的。我们研究了使用小型培训数据集建模双体内螺旋桨或三体系统的框架,与同行相比,我们的模型实现了最佳的数据效率和准确性性能。我们还将模型重新组织为建模多体和多体系统的扩展,展示了我们框架的可重复使用功能。
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.