Latent-Lagrangian 神经网络用于非自治非线性动力系统降阶建模
Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systems
这篇 arXiv 论文搞了个隐空间版 Lagrangian 神经网络，训练不用 ODE 求解器，对没见过的外力也能泛化，做物理建模的可以看看。
论文提出一种基于隐空间 Lagrangian 的降阶建模框架，面向受外力驱动的非线性动力系统。方法同时学习一组隐坐标和两个分别表示隐动能与隐势能的神经网络，并通过力监督在训练中省去 ODE 求解器。隐空间的物理一致性由虚功原理保证。结果显示该模型能学到系统非线性和非凸势能引起的细微动力学，并对未见过的外力和初始条件具有泛化能力。
Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systems
This work proposes a latent Lagrangian-based framework for reduced-order modelling of forced nonlinear dynamical systems. In contrast with conventional Lagrangian or Hamiltonian neural networks, our approach learns a set of latent coordinates sufficient to capture the dynamics conjointly with two neural networks for the latent kinetic and latent potential energies, and leverages force supervision to eliminate the need for an ODE solver during training. Consistency of physical laws in the latent space is ensured through the principle of virtual work. Results show that the model effectively learns the subtle dynamics induced by the system's nonlinearity and non-convex potential energy, and generalizes well to unseen forces and initial conditions. These observations confirm the physical relevance of the proposed approach, and its interest for model reduction.
