Deep learning of parameterized equations with applications to uncertainty quantification

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

doi:10.1615/int.j.uncertaintyquantification.2020034123

Deep learning of parameterized equations with applications to uncertainty quantification

Journal Article · Mon Feb 01 00:00:00 UTC 2021 · International Journal for Uncertainty Quantification

DOI:https://doi.org/10.1615/int.j.uncertaintyquantification.2020034123· OSTI ID:1738923

Qin, Tong ^[1]; Chen, Zhen ^[1]; Jakeman, John ^[2]; Xiu, Dongbin ^[1]

The Ohio State Univ., Columbus, OH (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

We propose a learning algorithm for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in particular those using deep neural network (DNN). We propose a DNN structure, largely based upon the residual network (ResNet), to not only learn the unknown form of the governing equation but also take into account the random effect embedded in the system, which is generated by the random parameters. Once the DNN model is successfully constructed, it is able to produce system prediction over longer term and for arbitrary parameter values. For uncertainty quantification, it allows us to conduct uncertainty analysis by evaluating solution statistics over the parameter space.

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

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

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1738923

Report Number(s):: SAND--2020-10596J; 691098

Journal Information:: International Journal for Uncertainty Quantification, Journal Name: International Journal for Uncertainty Quantification Journal Issue: 2 Vol. 11; ISSN 2152-5080

Publisher:: Begell HouseCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
deep neural network
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uncertainty quantification

Deep learning of parameterized equations with applications to uncertainty quantification

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