Data-driven discovery and extrapolation of parameterized pattern-forming dynamics

We develop a data-driven approach SINDyCP to discover dynamics for systems with adjustable control parameters, such as an external driving strength. We demonstrate the method on systems of varying complexity, ranging from discrete maps to systems of partial differential equations. To mitigate the impact of measurement noise, we also develop a weak formulation of SINDyCP and assess it's performance on noisy data. Applications include the discovery of universal pattern-formation equations from experimental data and extrapolation beyond the weakly nonlinear regime near the onset of an instability.