Doris Voina: Dynamic SINDy: latent variable discovery in noisy and nonlinear systems

Описание: Title: Dynamic SINDy: latent variable discovery in noisy and nonlinear systems.

Abstract
A significant challenge in many fields of science and engineering is making sense
of time-dependent measurement data by recovering governing equations in the
form of differential equations. We focus on finding parsimonious ordinary differen-
tial equation (ODE) models for nonlinear, noisy, and non-autonomous dynamical
systems and propose a machine learning method for data-driven system identifica-
tion. While many methods tackle noisy and limited data, non-stationarity – where
differential equation parameters change over time – has received less attention.
Our method, dynamic SINDy, combines variational inference with SINDy (sparse
identification of nonlinear dynamics) to model time-varying coefficients of sparse
ODEs. This framework allows for uncertainty quantification of ODE coefficients,
expanding on previous methods for autonomous systems. These coefficients are
then interpreted as latent variables and added to the system to obtain an autonomous
dynamical model. We validate our approach using synthetic data, including nonlin-
ear oscillators and the Lorenz system, and apply it to neuronal activity data from
C. elegans. Dynamic SINDy uncovers a global nonlinear model, showing it can
handle real, noisy, and chaotic datasets. We aim to apply our method to a variety of
problems, specifically dynamic systems with complex time-dependent parameters.