This paper is devoted to the derivation of computational methods for constructing partial differential equations from data. Following some recent works [7,14,15,20], we propose a methodology based on symbolic calculus [8,9,13], pseudospectral methods [2,3] and stochastic processes [6], in order to determine non-constant coefficients of linear evolution Partial Differential Equations (PDEs), from a set of structured data constituted by solutions at given times and positions, of an unknown linear PDE.

Additional Metadata
Keywords Inverse problems, Numerical approximation, Operator symbols, Partial differential equations, Pseudospectral methods
Persistent URL dx.doi.org/10.1016/j.jcp.2019.04.049
Journal Journal of Computational Physics
Citation
Lorin, E. (2019). From structured data to evolution linear partial differential equations. Journal of Computational Physics, 393, 162–185. doi:10.1016/j.jcp.2019.04.049