Paper Info
Title
Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data
Abstract
The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements compromise the accuracy and robustness of the model discovery procedure. In this work we develop a variant of the SINDy algorithm that integrates automatic differentiation and recent time-stepping constrained motivated by Rudy et al (2019 J. Computat. Phys. 396 483-506) for simultaneously (1) denoising the data, (2) learning and parametrizing the noise probability distribution, and (3) identifying the underlying parsimonious dynamical system responsible for generating the time-series data. Thus within an integrated optimization framework, noise can be separated from signal, resulting in an architecture that is approximately twice as robust to noise as state-of-the-art methods, handling as much as 40% noise on a given time-series signal and explicitly parametrizing the noise probability distribution. We demonstrate this approach on several numerical examples, from Lotka-Volterra models to the spatio-temporal Lorenz 96 model. Further, we show the method can learn a diversity of probability distributions for the measurement noise, including Gaussian, uniform, Gamma, and Rayleigh distributions.
Year
DOI
Venue
2022
10.1088/2632-2153/ac567a
MACHINE LEARNING-SCIENCE AND TECHNOLOGY
Keywords
DocType
Volume
automatic differentiation, denoising, nonlinear dynamics, optimization, sparse identification, machine learning, discrepancy modeling
Journal
3
Issue
Citations 
PageRank 
1
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Kadierdan Kaheman100.34
S. L. Brunton214123.92
J. Nathan Kutz322547.13