Sparse identification of a predator-prey system from simulation data of a convection model

Abstract

The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We utilize a data-driven modeling approach to identify a reduced model from simulation data of a convection problem. A convection model with a pressure source centered at the inner boundary models the edge dynamics of a magnetically confined plasma. The convection problem undergoes a sequence of bifurcations as the strength of the pressure source increases. The time evolution of the energies of the pressure profile, the turbulent flow, and the zonal flow capture the fundamental dynamic behavior of the full system. By applying the Sparse Identification of Nonlinear Dynamics (SINDy) method we identify a predator-prey type dynamical system that approximates the underlying dynamics of the three energy state variables. A bifurcation analysis of the system reveals consistency between the bifurcation structures, observed for the simulation data, and the identified underlying system.

Effect of enhanced dissipation by shear flows on transient relaxation and probability density function in two dimensions

“…For example, stable shear flows can dramatically quench turbulent transport by shear-induced-enhanced-dissipation (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]). This occurs as a shear flow distorts fluid eddies, accelerates the formation of small scales, and dissipates them when a molecular diffusion becomes effective on small scales.…”

On the Convergence of the SINDy Algorithm

“…In [17], the authors proposed an adaptive SINDy algorithm for discovering PDE, which iteratively applies ridge regression with hard thresholding. Additional approaches for model identification can be found in [5,8,10,11,14,16,22,24].…”

Methods for data-driven multiscale model discovery for materials

“…Loiseau et al [49] also demonstrated the ability of SINDy to identify dynamical systems models of high-dimensional systems, such as fluid flows, from a few physical sensor measurements. SINDy has also been applied to identify models in nonlinear optics [50] and plasma physics [51]. For actuated systems, SINDy has been generalized to include inputs and control [52], and these models are highly effective for model predictive control [53].…”