{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T06:15:45Z","timestamp":1770876945375,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:00:00Z","timestamp":1769817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":".S. Department of Energy, Office of Science, Office of 373 Nuclear Physics","award":["DE-AC02-05CH11231"],"award-info":[{"award-number":["DE-AC02-05CH11231"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we consider the optimization of non-invariant systems with both safety and control constraints. We present a new approach based on Bayesian optimization for the dynamic, safe and controlled optimization of such systems. Although there are other possible use cases, we focus on the application to the electron cyclotron resonance ion source VENUS. From experimental data, we have observed that VENUS behaves to first order as a non-invariant dynamic system with moving areas of instability. Our novel approach aims at providing a tool that can maintain system optimization in a safe way. This is accomplished by making sure the objective function, the beam current in the case of VENUS, does not fall under an operational minimum, while simultaneously requiring the optimization to avoid areas where VENUS is unstable. We compare the result of our approach on synthetic data modeled to mimic the behavior of VENUS with two methods from the literature, a standard Bayesian optimizer and a safe Bayesian optimizer, both adapted to deal with dynamic systems. A cross Student T-test is conducted to show the significance of the improvement given by the new method we introduce here, regarding the two preexisting methods we compared to. The results of the tests conducted on synthetic data show that the proposed method succeeds at maintaining the system optimized and obeys the predefined constraints better than the literature methods explored.<\/jats:p>","DOI":"10.3390\/axioms15020104","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T09:00:33Z","timestamp":1770022833000},"page":"104","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Optimization of Non-Invariant Systems with Constraints Developed for Application to the ECR Ion Source VENUS"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1122-1258","authenticated-orcid":false,"given":"Victor","family":"Watson","sequence":"first","affiliation":[{"name":"Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3577-4316","authenticated-orcid":false,"given":"Christopher M.","family":"Campbell","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7765-4235","authenticated-orcid":false,"given":"Heather L.","family":"Crawford","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5610-2327","authenticated-orcid":false,"given":"Yue Shi","family":"Lai","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2484-4606","authenticated-orcid":false,"given":"Marco","family":"Salathe","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-6684-8141","authenticated-orcid":false,"given":"Damon","family":"Todd","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1002\/xrs.3049","article-title":"Review of highly charged ion production with ECR ion source and the future opportunities for HCI physics","volume":"49","author":"Sun","year":"2019","journal-title":"X-Ray Spectrom."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"02A201","DOI":"10.1063\/1.3271135","article-title":"The third generation superconducting 28 GHz electron cyclotron resonance ion source VENUS (invited)","volume":"81","author":"Lyneis","year":"2010","journal-title":"Rev. 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