Data-Driven Learning of Nonautonomous Systems

Qin, Tong; Chen, Zhen; Jakeman, John D.; Xiu, Dongbin

doi:10.1137/20m1342859

Data-Driven Learning of Nonautonomous Systems

Journal Article · 06 May 2021 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/20m1342859· OSTI ID:1883180

^[1]; Chen, Zhen ^[2]; Jakeman, John D. ^[3]; Xiu, Dongbin ^[2]

Univ. of Michigan, Ann Arbor, MI (United States)
The Ohio State Univ., Columbus, OH (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

In this work, we present a numerical framework for recovering unknown nonautonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the nonautonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA); US Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: NA0003525; FA9550-18-1-0102

OSTI ID:: 1883180

Report Number(s):: SAND2021-11696J; 699538

Journal Information:: SIAM Journal on Scientific Computing, Vol. 43, Issue 3; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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