Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the Sparse Identification of Nonlinear Dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane $\nesepm$ and the electron temperature at the outer divertor $\tesepa$. Note that $\tesepa$ is not necessarily the peak value of $T_e$ along the divertor. The identified reduced models are interpretable by construction (i.e., not black box), and have the form of coupled ordinary differential equations (ODEs). Despite significant noise in $\tesepa$, the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5$\%$ in $\nesepm$ and 5 - 10$\%$ in $\tesepa$ for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A Model Predictive Control (MPC) strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in $\nesepm$ using the Integrated Plasma Simulator (IPS) framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely, SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).