{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:05:28Z","timestamp":1760148328510,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T00:00:00Z","timestamp":1681862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Data for complex plasma\u2013wall interactions require long-running and expensive computer simulations. Furthermore, the number of input parameters is large, which results in low coverage of the (physical) parameter space. Unpredictable occasions of outliers create a need to conduct the exploration of this multi-dimensional space using robust analysis tools. We restate the Gaussian process (GP) method as a Bayesian adaptive exploration method for establishing surrogate surfaces in the variables of interest. On this basis, we expand the analysis by the Student-t process (TP) method in order to improve the robustness of the result with respect to outliers. The most obvious difference between both methods shows up in the marginal likelihood for the hyperparameters of the covariance function, where the TP method features a broader marginal probability distribution in the presence of outliers. Eventually, we provide first investigations, with a mixture likelihood of two Gaussians within a Gaussian process ansatz for describing either outlier or non-outlier behavior. The parameters of the two Gaussians are set such that the mixture likelihood resembles the shape of a Student-t likelihood.<\/jats:p>","DOI":"10.3390\/e25040685","type":"journal-article","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T03:25:11Z","timestamp":1681961111000},"page":"685","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Outlier-Robust Surrogate Modeling of Ion\u2013Solid Interaction Simulations"],"prefix":"10.3390","volume":"25","author":[{"given":"Roland","family":"Preuss","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Plasmaphysik, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8867-1014","authenticated-orcid":false,"given":"Udo","family":"von Toussaint","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Plasmaphysik, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,19]]},"reference":[{"unstructured":"Reiter, D. (2019, September 13). The EIRENE Code User Manual. Manual Version. Available online: http:\/\/www.eirene.de\/manuals\/eirene.pdf.","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Preuss, R., and von Toussaint, U. (2021). Global Variance as a Utility Function in Bayesian Optimization. Phys. Sci. Forum, 3.","key":"ref_2","DOI":"10.3390\/psf2021003003"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s41060-018-0119-9","article-title":"Stable Bayesian optimization","volume":"6","author":"Nguyen","year":"2018","journal-title":"Int. J. Data Sci. 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Proceedings of the 24h International Conference on Machine Learning, Corvallis, OR, USA.","key":"ref_7"},{"key":"ref_8","first-page":"877","article-title":"Student-t Processes as Alternatives to Gaussian Processes","volume":"Volume 33","author":"Shah","year":"2014","journal-title":"Proceedings of the 17th International Conference on Artificial Intelligence and Statistics"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1093\/biomet\/55.1.119","article-title":"A Bayesian approach to some outlier problems","volume":"55","author":"Box","year":"1968","journal-title":"Biometrika"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.jprocont.2019.06.007","article-title":"Gaussian process modelling with Gaussian mixture likelihood","volume":"81","author":"Daemi","year":"2019","journal-title":"J. Process. Control."},{"unstructured":"Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (2007). 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Outlier-Robust Surrogate Modelling of Ion-Solid Interaction Simulations. Phys. Sci. Forum, 5.","key":"ref_15","DOI":"10.3390\/psf2022005035"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1049\/ip-vis:19941330","article-title":"Novelty detection and neural network validation","volume":"141","author":"Bishop","year":"1994","journal-title":"IEE Proc. Vision Image Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10115-006-0036-4","article-title":"Detecting anomalies in cross-classified streams: A Bayesian approach","volume":"11","author":"Agarwal","year":"2006","journal-title":"Knowl. Inf. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1002\/aic.13887","article-title":"A Bayesian approach to robust process identification with ARX models","volume":"59","author":"Khatibisepehr","year":"2013","journal-title":"AIChE J."},{"doi-asserted-by":"crossref","unstructured":"Terry, N., and Choe, Y. (2021). Splitting Gaussian processes for computationally-efficient regression. PLoS ONE, 16.","key":"ref_19","DOI":"10.1371\/journal.pone.0256470"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/4\/685\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:18:51Z","timestamp":1760123931000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/4\/685"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,19]]},"references-count":19,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["e25040685"],"URL":"https:\/\/doi.org\/10.3390\/e25040685","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,4,19]]}}}