Doris Voina: Dynamic SINDy: latent variable discovery in noisy and nonlinear systems скачать в хорошем качестве

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

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.