Bringing advanced sparse system identification to plasma physics

Many tasks in fluid and plasma physics, such as design optimization and control, are challenging because of nonlinearity and a large range of scales in both space and time. This range of scales necessitates exceedingly high-dimensional measurements and computational discretization to resolve all relevant features, resulting in vast data sets and time-intensive computations. Machine learning constitutes a growing set of powerful techniques to extract patterns and build models from nonlinear systems data, complementing existing theoretical, numerical, and experimental efforts. The sparse identification of nonlinear dynamics (SINDy) algorithm is one such method that identifies a minimal dynamical system model while balancing model complexity with accuracy, avoiding overfitting. This approach tends to promote models that are interpretable and generalizable, capturing the essential physics of the system. We discuss recent advances with the SINDy method, including the identification of PDE systems, the incorporation of physical constraints from global conservation laws, promoting global stability, solving for weak-formulation differential equations, and more. These advances have been consolidated into the open-source PySINDy code, enabling anyone with access to measurement data to engage in scientific model discovery. We conclude with recent work that explores connections with permanent magnet optimization for stellarators.