论文标题
从稀疏观察到的数据中预测时空动力学的深度学习方法
A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data
论文作者
论文摘要
在本文中，我们考虑了由未知偏微分方程（PDE）驱动的时空物理过程学习预测模型的问题。我们提出了一个深度学习框架，该框架可以学习潜在的动态，并使用稀疏分布的数据站点来预测其进化。近年来，深度学习在建模物理动态方面表现出了令人鼓舞的结果。但是，大多数现有的深度学习方法用于建模物理动力学，要么是求解已知的PDE，要么在统治PDES尚不清楚时需要密集的网格中的数据。相比之下，我们的方法仅从稀疏观察到的数据中研究了未知PDE驱动的动态的学习预测模型。所提出的方法是空间维度无关的，几何柔性。我们在具有不同边界条件的多个几何形状和十维热量方程的多个几何形状中的二维波方程的预测任务中演示了我们的方法。
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and predicts its evolution using sparsely distributed data sites. Deep learning has shown promising results in modeling physical dynamics in recent years. However, most of the existing deep learning methods for modeling physical dynamics either focus on solving known PDEs or require data in a dense grid when the governing PDEs are unknown. In contrast, our method focuses on learning prediction models for unknown PDE-driven dynamics only from sparsely observed data. The proposed method is spatial dimension-independent and geometrically flexible. We demonstrate our method in the forecasting task for the two-dimensional wave equation and the Burgers-Fisher equation in multiple geometries with different boundary conditions, and the ten-dimensional heat equation.
