Interpretable nonlinear models of unsteady flow physics

Accurate and efficient reduced-order models are essential to understand, predict, estimate, and control unsteady fluid flows. These models should ideally be generalizable, interpretable, and based on limited training data. This talk will explore the sparse identification of nonlinear dynamics (SINDy) approach to uncover interpretable models for unsteady flow physics. First, we will discuss how it is possible to enforce known constraints, such as energy conserving quadratic nonlinearities, to essentially “bake in” known physics. Next, we will demonstrate that higher-order nonlinearities can approximate the effect of truncated modes, resulting in more accurate models of lower order than Galerkin projection. Finally, we will discuss the use of intrinsic measurement coordinates, such as lift, drag, and pressure, to build nonlinear models, circumventing the well-known issue of continuous mode deformation associated with methods based on the proper orthogonal decomposition. This approach will be demonstrated on several relevant flow configurations with low-dimensional dynamics.