Machine Learning to Discover Interpretable Models in Fluids and Plasmas

Many tasks in fluid and plasma physics, such as design optimization and control, are challenging because fluids and plasmas are nonlinear and exhibit 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. Indeed, fluid dynamics is one of the original big data fields, and many high-performance computing architectures, experimental measurement techniques, and advanced data processing and visualization algorithms were driven by decades of research in fluid mechanics. Machine learning constitutes a growing set of powerful techniques to extract patterns and build models from fluid and plasma 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 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.