论文标题
LASDI：参数潜在空间动力学标识
LaSDI: Parametric Latent Space Dynamics Identification
论文作者
论文摘要
通过数据启用快速准确的物理模拟已成为计算物理学的重要领域，以帮助逆问题，设计优化，不确定性量化和其他各种决策应用。本文为参数潜在空间动态标识过程提供了一个数据驱动的框架，该过程可以快速，准确地模拟。参数模型是通过构建一组本地潜在空间模型并设计它们之间的相互作用来实现的。单个本地潜在空间动力学模型在信任区域中实现了准确的解决方案。通过让一组信任区域覆盖整个参数空间，我们的模型显示出随着训练数据的增加而提高准确性。我们介绍了两种不同类型的交互机制，即基于点和区域的方法。使用线性和非线性数据压缩技术。我们说明了潜在空间动力学识别（LASDI）的框架，在各种偏微分方程（即汉堡方程，径向对流问题和非线性热传导问题）上实现了快速准确的解决方案过程，达到了$ O（100）$ x速度$ x加速和$ o（1）\％\％$相对于相应的成熟级别的误差。
Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. We introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers' equations, radial advection problem, and nonlinear heat conduction problem, achieving $O(100)$x speed-up and $O(1)\%$ relative error with respect to the corresponding full order models.
