LaSDI：参数化潜空间动力学辨识
LaSDI: Parametric Latent Space Dynamics Identification
摘要：
利用数据实现快速准确的物理模拟已成为计算物理学的一个重要领域，以帮助反问题，设计优化，不确定性量化和其他各种决策应用。本文提出了一个数据驱动的框架参数潜在的空间动力学识别过程，使快速和准确的模拟。参数化模型是通过建立一组局部潜在空间模型并设计它们之间的交互来实现的。个体局部潜空间动力学模型在置信域内实现精确解。通过让置信域集覆盖整个参数空间，我们的模型显示出随着训练数据的增加而增加的准确性。我们引入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，使各种偏微分方程，即，Burgers方程、径向对流问题和非线性热传导问题，实现了$O(100)$ ×加速和相对于相应全阶模型的$O(1)\%$相对误差。
英文摘要：
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.
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