Paper Info
Title
Deep learning of dynamics and signal-noise decomposition with time-stepping constraints.
Abstract
A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large volumes of data to average over the effect of noise. We propose a novel paradigm for data-driven modeling that simultaneously learns the dynamics and estimates the measurement noise at each observation. By constraining our learning algorithm, our method explicitly accounts for measurement error in the map between observations, treating both the measurement error and the dynamics as unknowns to be identified, rather than assuming idealized noiseless trajectories. We model the unknown vector field using a deep neural network, imposing a Runge-Kutta integrator structure to isolate this vector field, even when the data has a non-uniform timestep, thus constraining and focusing the modeling effort. We demonstrate the ability of this framework to form predictive models on a variety of canonical test problems of increasing complexity and show that it is robust to substantial amounts of measurement error. We also discuss issues with the generalizability of neural network models for dynamical systems and provide open-source code for all examples.
Year
DOI
Venue
2019
10.1016/j.jcp.2019.06.056
Journal of Computational Physics
Keywords
Field
DocType
Machine learning,Dynamical systems,Data-driven models,Neural networks,System identification,Deep learning
Noise reduction,Generalizability theory,Mathematical optimization,Vector field,Integrator,Algorithm,Dynamical systems theory,Artificial intelligence,Deep learning,Artificial neural network,Mathematics,Observational error
Journal
Volume
ISSN
Citations 
396
0021-9991
5
PageRank 
References 
Authors
0.44
14
3
Name
Order
Citations
PageRank
Samuel H. Rudy150.77
J. Nathan Kutz222547.13
S. L. Brunton314123.92