A CFL-type condition and theoretical insights for discrete-time sparse full-order model inference

• We provide theoretical insights on inferred sparse Full-Order Models for discrete time dynamical systems with a focus on accuracy and stability. • For one-dimensional linear advection, we formulate and validate an explicit ”sampling CFL” condition, connecting the stability of the sFOM to the spatial and temporal resolution of the training data. • We present numerical results on the sFOM inference for two nonlinear test cases (2D Burgers’ equation and incompressible cavity flow) and draw connections to our theoretical findings. In this work, we investigate the data-driven inference of a discrete-time dynamical system via a sparse Full-Order Model (sFOM). We first formulate the involved Least Squares (LS) problem and discuss the need for regularization, indicating a connection between the typically employed l 2 regularization and the stability of the inferred discrete-time sFOM. We then provide theoretical insights considering the consistency and stability properties of the inferred numerical schemes that form the sFOM and exemplify them via illustrative, 1D test cases of linear diffusion and linear advection. For linear advection, we analytically derive a “sampling CFL” condition, which dictates a bound for the ratio of spatial and temporal discretization steps in the training data that ensures stability of the inferred sFOM. Finally, we investigate the sFOM inference for two nonlinear problems, namely a 2D Burgers’ test case and the incompressible flow in an oscillating lid-driven cavity, and draw connections between the theoretical findings and the properties of the inferred, nonlinear sFOMs. Novelty statement: sparse FOM inference for dynamical systems in discrete time. Theoretical insights on the analytical solution of the sparse FOM least-squares problem. Established connection between the stability of sparse FOM and the l 2 regularization of the least-squares problem.