Session: CIE-04-01 - AMS: Uncertainty Quantification in Simulation and Model Verification & Validation

Paper Number: 89213

89213 - Integrated Computational Materials Engineering With Monotonic Gaussian Processes 

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 machine learning model requires significantly fewer 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 two different material datasets, where one experimental and one computational dataset is 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 is scarce and noisy or when the dimensionality is high, and monotonicity is where supported by strong physical reasoning.

Presenting Author: Anh Tran Sandia National Laboratories

Presenting Author Biography: Dr. Anh Tran is currently working at the Optimization and Uncertainty Quantification Department in Sandia National Laboratories, Albuquerque, NM. He obtained my B.S., M.S., and Ph.D. in Mechanical Engineering from Georgia Institute of Technology in December 2011 and December 2018, respectively. His research interests include uncertainty quantification, optimization, and machine learning methodologies, with multi-scale computational materials science applications.

Authors:

Anh Tran Sandia National Laboratories
Kathryn Maupin Sandia National Laboratories
Theron Rodgers Sandia National Laboratories