{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:11:15Z","timestamp":1760242275726,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,2,21]],"date-time":"2017-02-21T00:00:00Z","timestamp":1487635200000},"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>Within the Bayesian framework, we utilize Gaussian processes for parametric studies of long running computer codes. Since the simulations are expensive, it is necessary to exploit the computational budget in the best possible manner. Employing the sum over variances \u2014being indicators for the quality of the fit\u2014as the utility function, we establish an optimized and automated sequential parameter selection procedure. However, it is also often desirable to utilize the parallel running capabilities of present computer technology and abandon the sequential parameter selection for a faster overall turn-around time (wall-clock time). This paper proposes to achieve this by marginalizing over the expected outcomes at optimized test points in order to set up a pool of starting values for batch execution. For a one-dimensional test case, the numerical results are validated with the analytical solution. Eventually, a systematic convergence study demonstrates the advantage of the optimized approach over randomly chosen parameter settings.<\/jats:p>","DOI":"10.3390\/e19020084","type":"journal-article","created":{"date-parts":[[2017,2,22]],"date-time":"2017-02-22T11:40:52Z","timestamp":1487763652000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sequential Batch Design for Gaussian Processes Employing Marginalization \u2020"],"prefix":"10.3390","volume":"19","author":[{"given":"Roland","family":"Preuss","sequence":"first","affiliation":[{"name":"Max-Planck-Institute for Plasma Physics, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Udo","family":"Von Toussaint","sequence":"additional","affiliation":[{"name":"Max-Planck-Institute for Plasma Physics, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Barber, D. 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Mustererkennung 2000, Springer."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1198\/TECH.2009.0015","article-title":"Adaptive Design and Analysis of Supercomputer Experiments","volume":"51","author":"Gramacy","year":"2009","journal-title":"Technometrics"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Mockus, J. (1989). Bayesian Approach to Global Optimization, Springer.","DOI":"10.1007\/978-94-009-0909-0"},{"key":"ref_9","first-page":"409","article-title":"Design and Analysis of Computer Experiments","volume":"4","author":"Sacks","year":"1989","journal-title":"Stat. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1023\/A:1008294716304","article-title":"Bayesian Algorithms for One-Dimensional Global Optimization","volume":"10","author":"Locatelli","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_11","unstructured":"Lafferty, J.D., Williams, C.K.I., Shawe-Taylor, J., Zemel, R.S., and Culotta, A. (2010). Advances in Neural Information Processing Systems 23, Curran Associates."},{"key":"ref_12","unstructured":"Azimi, J., Jalali, A., and Fern, X. (July, January 26). Hybrid Batch Bayesian Optimization. Proceedings of the 29th International Conference on Machine Learning, Edinburgh, Scotland."},{"key":"ref_13","first-page":"790","article-title":"GLASSES: Relieving The Myopia of Bayesian Optimisation","volume":"51","author":"Gonzalez","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Rasmussen, C., and Williams, C. (2006). Gaussian Processes for Machine Learning, MIT Press.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"605","DOI":"10.13182\/FST15-178","article-title":"Gaussian Processes for SOLPS Data Emulation","volume":"69","author":"Preuss","year":"2016","journal-title":"Fusion Sci. Technol."},{"key":"ref_16","unstructured":"Coster, D. Private communication."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/2\/84\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:28:49Z","timestamp":1760207329000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/2\/84"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,21]]},"references-count":16,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,2]]}},"alternative-id":["e19020084"],"URL":"https:\/\/doi.org\/10.3390\/e19020084","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,2,21]]}}}