论文标题
从其解决方案中可以学习多少部分微分方程？
How much can one learn a partial differential equation from its solution?
论文作者
论文摘要
在这项工作中，我们研究了从其解决方案数据中学习部分微分方程（PDE）的问题。使用各种类型的PDE作为示例，以说明解决方案数据可以根据基础操作员和初始数据显示多少PDE操作员。提出了基于局部回归和全局一致性的数据驱动和数据自适应方法，以实现稳定的PDE识别。提供数值实验来验证我们的分析并证明所提出的算法的性能。
In this work we study the problem about learning a partial differential equation (PDE) from its solution data. PDEs of various types are used as examples to illustrate how much the solution data can reveal the PDE operator depending on the underlying operator and initial data. A data driven and data adaptive approach based on local regression and global consistency is proposed for stable PDE identification. Numerical experiments are provided to verify our analysis and demonstrate the performance of the proposed algorithms.
