Numerical Aspects for Approximating Governing Equations Using Data

Understand

We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data.

• We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high accuracy.
• Upon recasting the problem into a function approximation problem, we discuss several important aspects for accurate approximation.
• Most notably, we discuss the importance of using a large number of short bursts of trajectory data, rather than using data from a single long trajectory.