潜变量拉格朗日神经网络用于非自治非线性动力系统的降阶建模
Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systems
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中文总结 AI 辅助
本文提出潜变量拉格朗日神经网络框架，通过学习潜坐标与能量函数，结合力监督，实现受迫非线性动力系统的降阶建模，并验证了其泛化能力。
中文摘要 AI 辅助
本文提出了一种基于潜变量拉格朗日框架的降阶建模方法，用于受迫非线性动力系统。与传统拉格朗日或哈密顿神经网络不同，我们的方法学习一组足以捕捉动力学的潜坐标，同时使用两个神经网络分别表示潜动能和潜势能，并利用力监督来消除训练过程中对常微分方程求解器的需求。通过虚功原理确保潜空间中物理定律的一致性。结果表明，该模型能有效学习由系统非线性和非凸势能引起的细微动力学，并能很好地泛化到未见过的力和初始条件。这些观察结果证实了所提方法的物理相关性及其在模型降阶方面的价值。
英文摘要
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.
发表机构
- Université Paris-Saclay（巴黎萨克雷大学）
- CEA List（法国原子能委员会信息技术与系统实验室）
机构由 AI 辅助整理，请以论文原文为准。
