Derivative-based SINDy (DSINDy): Addressing the challenge of discovering governing equations from noisy data

Understand

Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements.

• One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a predetermined basis in the states and finds the expansion coefficients through linear regression with sparsity constraints.
• This approach requires an accurate estimation of the state time derivatives, which is not necessarily possible in the high-noise regime without additional constraints.
• We present an approach called Derivative-based SINDy (DSINDy) that combines two novel methods to improve ODE recovery at high noise levels.