Time-series machine-learning error models for approximate solutions to parameterized dynamical systems

Journal Article · Sat Mar 28 00:00:00 EDT 2020 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2020.112990· OSTI ID:1619214

Parish, Eric J. ^[1]; Carlberg, Kevin T. ^[2]

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1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2. Univ. of Washington, Seattle, WA (United States)

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in Ref. Freno and Carlberg (2019) to dynamical systems. The proposed Time-Series Machine-Learning Error Modeling (T-MLEM) method constructs a regression model that maps features – which comprise error indicators that are derived from standard a posteriori error-quantification techniques – to a random variable for the approximate-solution error at each time instance. The proposed framework considers a wide range of candidate features, regression methods, and additive noise models. We consider primarily recursive regression techniques developed for time-series modeling, including both classical time-series models (e.g., autoregressive models) and recurrent neural networks (RNNs), but also analyze standard non-recursive regression techniques (e.g., feed-forward neural networks) for comparative purposes. Finally, numerical experiments conducted on multiple benchmark problems illustrate that the long short-term memory (LSTM) neural network, which is a type of RNN, outperforms other methods and yields substantial improvements in error predictions over traditional approaches.

• Research Organization: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1619214
• Alternate ID(s): OSTI ID: 1776372
• Report Number(s): SAND--2019-8804J; 677948
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 365; ISSN 0045-7825
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
error modeling
long short-term memory networks
model reduction
parameterized dynamical systems
recurrent neural networks
time-series modeling