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To address these challenges, we present SCOUT-Nd (<jats:underline>S<\/jats:underline>tochastic <jats:underline>C<\/jats:underline>onstrained <jats:underline>O<\/jats:underline>p<jats:underline>t<\/jats:underline>imization for N dimensions), a gradient-based algorithm that can be used on non-differentiable objectives. It can be combined with natural gradients in order to further enhance convergence properties. and it also incorporates multi-fidelity schemes and an adaptive selection of samples in order to minimize computational effort. We validate our approach using standard, benchmark problems, demonstrating its superior performance in parameter optimization compared to existing methods. Additionally, we showcase the algorithm\u2019s efficacy in a complex real-world application, i.e. the optimization of a wind farm layout.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad8e2b","type":"journal-article","created":{"date-parts":[[2024,11,2]],"date-time":"2024-11-02T22:54:03Z","timestamp":1730588043000},"page":"015024","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Stochastic black-box optimization using multi-fidelity score function estimator"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9101-359X","authenticated-orcid":true,"given":"Atul","family":"Agrawal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1927-7651","authenticated-orcid":true,"given":"Kislaya","family":"Ravi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9345-759X","authenticated-orcid":false,"given":"Phaedon-Stelios","family":"Koutsourelakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0171-0712","authenticated-orcid":false,"given":"Hans-Joachim","family":"Bungartz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2025,1,31]]},"reference":[{"key":"mlstad8e2bbib1","doi-asserted-by":"publisher","first-page":"30055","DOI":"10.1073\/pnas.1912789117","article-title":"The frontier of simulation-based inference","volume":"117","author":"Cranmer","year":"2020","journal-title":"Proc. of the National Academy of Sciences Proc. 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