Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications
- 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.
- Research Organization:
- Sandia National Lab. (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, Vol. 23, Issue 1; ISSN 1530-9827
- Publisher:
- ASMECopyright Statement
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
36 MATERIALS SCIENCE
Machine Intelligence for Engineering Under Uncertainties
artificial intelligence
data-driven engineering
engineering informatics
machine learning for engineering applications
multiphysics modeling and simulation
machine learning
materials science
physics
stress
testing
crystals
plasticity
simulation
noise (Sound)
finite element analysis
interpolation