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.

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Journal of Computational Physics
School of Mathematics and Statistics

Lorin, E. (2019). From structured data to evolution linear partial differential equations. Journal of Computational Physics, 393, 162–185. doi:10.1016/