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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.<\/jats:p>","DOI":"10.1115\/1.4055852","type":"journal-article","created":{"date-parts":[[2022,10,5]],"date-time":"2022-10-05T05:11:10Z","timestamp":1664946670000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":8,"title":["Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications"],"prefix":"10.1115","volume":"23","author":[{"given":"Anh","family":"Tran","sequence":"first","affiliation":[{"name":"Sandia National Laboratories Scientific Machine Learning, , Albuquerque, NM 87185"}]},{"given":"Kathryn","family":"Maupin","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories Optimization and Uncertainty Quantification, , Albuquerque, NM 87185"}]},{"given":"Theron","family":"Rodgers","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories Computational Materials & Data Science, , Albuquerque, NM 87185"}]}],"member":"33","published-online":{"date-parts":[[2022,10,20]]},"reference":[{"volume-title":"Materials Genome Initiative for Global Competitiveness","year":"2011","author":"National Science and Technology Council (US)","key":"2023102000105172200_CIT0001"},{"issue":"8","key":"2023102000105172200_CIT0002","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1080\/09506608.2016.1191808","article-title":"Six Decades of the Hall\u2013Petch Effect\u2014A Survey of Grain-Size Strengthening Studies on Pure Metals","volume":"61","author":"Cordero","year":"2016","journal-title":"Int. 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