Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures
Yunan Yang, Levon Nurbekyan, Elisa Negrini, Robert Martin, Mirjeta Pasha
Abstract
.We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data are not sufficient for estimating time derivatives of state variables but enough to approximate the long-time behavior of the system through an approximation of its physical measure. Thus, we fit physical measures by taking the Wasserstein distance from optimal transportation as a misfit function between two probability distributions. In particular, we analyze the regularity of the resulting loss function for general transportation costs and derive gradient formulas. Physical measures are approximated as fixed points of suitable PDE-based Perron–Frobenius operators. Test cases discussed in the paper include common low-dimensional dynamical systems.Keywordsdynamical systemparameter identificationoptimal transportationWasserstein metriccontinuity equationinverse problemsMSC codes37M2149Q2282C3134A5565N0893B30