论文标题
用于学习物理系统非线性动态的变异自动编码器
Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems
论文作者
论文摘要
我们开发了数据驱动的方法，用于合并先验的物理信息，以学习由参数化的PDE和力学引起的非线性系统的简约表示。我们的方法是基于各种自动编码器（VAE），用于从观察结果中学习非线性状态空间模型。我们开发通过一般歧管的潜在空间表示来纳入几何和拓扑先验的方法。我们研究了我们为非线性汉堡方程和约束机械系统学习低维表示方法的方法的性能。
We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.
