|Title: How much can one learn a PDE from its solution?|
|Seminar: Analysis and Differential Geometry|
|Speaker: Yimin Zhong of Auburn University|
|Contact: Yiran Wang, email@example.com|
|Date: 2022-12-01 at 4:00PM|
|Venue: PAIS 230|
In this work we study a few basic questions for PDE learning from observed solution data. Using various types of PDEs, we show 1) how the approximate dimension (richness) of the data space spanned by all snapshots along a solution trajectory depends on the differential operator and initial data, and 2) identifiability of a differential operator from solution data on local patches. Then we propose a consistent and sparse local regression method (CaSLR) for general PDE identification. Our method is data driven and requires minimal amount of local measurements in space and time from a single solution trajectory by enforcing global consistency and sparsity.
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