论文标题
GD-VAE：用于学习非线性动力学和降低尺寸的几何动力学自动编码器
GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions
论文作者
论文摘要
我们开发了包含几何和拓扑信息的数据驱动方法，以从观测值中学习非线性动力学的偏爱表示。这些方法使用与变异自动编码器（VAES）相关的训练策略学习了通用歧管潜在空间动力学的非线性状态空间模型。我们的方法称为几何动力学（GD）变化自动编码器（GD-VAE）。我们基于深层神经网络体系结构学习系统状态和进化的编码器和解码器，包括一般多层感知器（MLP），卷积神经网络（CNN）和其他体系结构。由参数化的PDE和物理学引起的问题所激发，我们研究了学习方法的性能，用于学习的任务降低了非线性汉堡方程，机械系统约束的机械系统和反应扩散系统的空间场。 GD-VAE提供的方法可用于在涉及动态的各种学习任务中获取多种潜在空间中的表示形式。
We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and other architectures. Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning reduced dimensional representations of the nonlinear Burgers Equations, Constrained Mechanical Systems, and spatial fields of Reaction-Diffusion Systems. GD-VAEs provide methods that can be used to obtain representations in manifold latent spaces for diverse learning tasks involving dynamics.
