Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

Tran, Anh; Maupin, Kathryn; Rodgers, Theron

doi:10.1115/1.4055852

Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

Journal Article · 20 October 2022 · Journal of Computing and Information Science in Engineering

DOI:https://doi.org/10.1115/1.4055852· OSTI ID:1887418

Tran, Anh ^[1]; Maupin, Kathryn ^[1]; Rodgers, Theron ^[1]

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

Physics-constrained machine learning is emerging as an important topic in the field of machine learning for physics. One of the most significant advantages of incorporating physics constraints into machine learning methods is that the resulting model requires significantly less data to train. By incorporating physical rules into the machine learning formulation itself, the predictions are expected to be physically plausible. Gaussian process (GP) is perhaps one of the most common methods in machine learning for small datasets. In this paper, we investigate the possibility of constraining a GP formulation with monotonicity on three different material datasets, where one experimental and two computational datasets are used. The monotonic GP is compared against the regular GP, where a significant reduction in the posterior variance is observed. The monotonic GP is strictly monotonic in the interpolation regime, but in the extrapolation regime, the monotonic effect starts fading away as one goes beyond the training dataset. Imposing monotonicity on the GP comes at a small accuracy cost, compared to the regular GP. The monotonic GP is perhaps most useful in applications where data are scarce and noisy, and monotonicity is supported by strong physical evidence.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 1887418

Report Number(s):: SAND2022-12090J; 709665

Journal Information:: Journal of Computing and Information Science in Engineering, Journal Name: Journal of Computing and Information Science in Engineering Journal Issue: 1 Vol. 23; ISSN 1530-9827

Publisher:: ASMECopyright Statement

Country of Publication:: United States

Language:: English

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Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

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