IDENT: Identifying Differential Equations with Numerical Time evolution

Understand

Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem.

• A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying coefficients add complexity to the problem.
• We assume that the governing partial differential equation (PDE) is a linear combination of a subset of a prescribed dictionary containing different differential terms, and the objective of this paper is to find the correct coefficients.
• We propose a new direction based on the fundamental idea of convergence analysis of numerical PDE schemes.