DATA-DRIVEN SPATIALLY DEPENDENT PDE IDENTIFICATION

We propose a data-driven partial differential equation (PDE) identification scheme based on $\ell_1$-norm minimization which can identify spatially-dependent PDEs from measurements. Spatially-dependent PDEs refers to that the terms in the PDEs vary across space. In reality a physical system is often governed by spatially-dependent PDEs because the properties of the medium can be various across space, and the proposed method is the first data-driven spatially-dependent PDEs identification scheme. In addition, our method is efficient owing to its non-iterative nature and efficient implementation by coordinate descent.