{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T03:47:43Z","timestamp":1791776863397,"version":"4.3.4"},"reference-count":35,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,10,11]],"date-time":"2026-10-11T00:00:00Z","timestamp":1791676800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,11]],"date-time":"2026-10-11T00:00:00Z","timestamp":1791676800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["advanced.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Advanced Science"],"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Scientific optimization problems are often characterized by slow, expensive, and non\u2010differentiable evaluations, which severely limit efficient exploration of rich design spaces. In these settings, performance depends not only on the optimizer itself, but also on whether the chosen search space can represent good solutions and whether important design requirements are effectively incorporated into the search. Here, we introduce a gradient\u2010free optimization framework based on large language models (LLMs) that enables the generation and refinement of executable control policies directly from natural language. We propose two complementary paradigms: Prompt\u2010to\u2010Optimizer (P2O), which combines LLM\u2010based structural generation with gradient\u2010free parameter optimization, and Prompt\u2010to\u2010Protocol (P2P), which directly synthesizes fully specified control policies. We apply this framework to battery fast\u2010charging protocol design, a representative slow\u2010feedback optimization problem. Across multiple case studies, our methods outperform conventional approaches restricted to predefined functional forms. In a realistic fast\u2010charging scenario, both approaches improve battery state of health by approximately 4.2% over a representative baseline, with P2P achieving this under matched evaluation budgets. More broadly, our results suggest that LLMs can serve as representation generators that expand the hypothesis space of scientific optimization, enabling efficient search in domains where evaluations are costly, and gradients are\u00a0unavailable.<\/jats:p>","DOI":"10.1002\/advs.78012","type":"journal-article","created":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T03:24:38Z","timestamp":1791775478000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["LLMs as Representation Generators for Gradient\u2010Free Scientific Optimization: A Case Study in Battery Fast Charging"],"prefix":"10.1002","author":[{"given":"Ge","family":"Lei","sequence":"first","affiliation":[{"name":"Dyson School of Design Engineering Imperial College London London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6363-2812","authenticated-orcid":false,"given":"Ferran","family":"Brosa Planella","sequence":"additional","affiliation":[{"name":"The Faraday Institution Harwell Campus  Didcot UK"},{"name":"Mathematics Institute University of Warwick  Gibbet Hill Road Coventry CV4 7AL UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4491-6876","authenticated-orcid":false,"given":"Sterling G.","family":"Baird","sequence":"additional","affiliation":[{"name":"Acceleration Consortium University of Toronto Toronto Ontario Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4055-6903","authenticated-orcid":false,"given":"Samuel J.","family":"Cooper","sequence":"additional","affiliation":[{"name":"Dyson School of Design Engineering Imperial College London London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,11]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.est.2016.02.005"},{"key":"e_1_2_8_3_1","article-title":"Impact of Charging Rates on Electric Vehicle Battery Life","volume":"2021","author":"Mothilal Bhagavathy S.","year":"2021","journal-title":"Findings"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-33486-4"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-025-92738-7"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.3390\/batteries11010006"},{"issue":"1","key":"e_1_2_8_7_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/S0378-7753(03)00027-2","article-title":"Comparison of the Capacity Fade of Sony US 18650 Cells Charged With Different Protocols","volume":"122","author":"Sikha G.","year":"2003","journal-title":"Journal of Power Sources"},{"issue":"2","key":"e_1_2_8_8_1","doi-asserted-by":"crossref","first-page":"54","DOI":"10.3390\/wevj15020054","article-title":"Comparison of EV Fast Charging Protocols and Impact of Sinusoidal Half\u2010Wave Fast Charging Methods on Lithium\u2010Ion Cells","volume":"15","author":"Althurthi S. B.","year":"2024","journal-title":"World Electric Vehicle Journal"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-020-1994-5"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1021\/acssuschemeng.4c01673"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpowsour.2023.233272"},{"issue":"12","key":"e_1_2_8_12_1","doi-asserted-by":"crossref","DOI":"10.1007\/s11704-026-60308-3","article-title":"A Survey of Large Language Models","volume":"20","author":"Zhao W. X.","year":"2026","journal-title":"Frontiers of Computer Science"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586\u2010023\u201006924\u20106"},{"key":"e_1_2_8_14_1","doi-asserted-by":"crossref","unstructured":"R.Lange Y.Tian andY.Tang \u201cLarge Language Models as Evolution Strategies \u201d inProceedings of the Genetic and Evolutionary Computation Conference Companion(2024) 579\u2013582.","DOI":"10.1145\/3638530.3654238"},{"key":"e_1_2_8_15_1","article-title":"Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap","author":"Wu X.","year":"2024","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"e_1_2_8_16_1","doi-asserted-by":"crossref","first-page":"0646","DOI":"10.34133\/research.0646","article-title":"When Large Language Models Meet Evolutionary Algorithms: Potential Enhancements and Challenges","volume":"8","author":"Wang C.","year":"2025","journal-title":"Research"},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.xcrp.2024.101844"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1021\/acsmaterialslett.4c02674"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.1039\/D5TA05224F"},{"key":"e_1_2_8_20_1","unstructured":"J.Qian H.Wang Z.Li S.Li andX.Yan \u201cLimitations of Language Models in Arithmetic and Symbolic Induction \u201d arXiv Preprint arXiv:2208.05051 (2022)."},{"key":"e_1_2_8_21_1","doi-asserted-by":"crossref","unstructured":"T.Baeumel J.vanGenabith andS.Ostermann \u201cThe Lookahead Limitation: Why Multi\u2010Operand Addition Is Hard for LLMs \u201d arXiv Preprint arXiv:2502.19981 (2025).","DOI":"10.18653\/v1\/2025.blackboxnlp-1.15"},{"key":"e_1_2_8_22_1","doi-asserted-by":"crossref","unstructured":"A.Gambardella Y.Iwasawa andY.Matsuo \u201cLanguage Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks \u201d arXiv Preprint arXiv:2406.02356 (2024).","DOI":"10.18653\/v1\/2024.acl-short.8"},{"key":"e_1_2_8_23_1","unstructured":"D.ErikssonandM.Jankowiak \u201cHigh\u2010Dimensional Bayesian Optimization With Sparse Axis\u2010Aligned Subspaces \u201d (2021) arxiv:2103.00349."},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.commatsci.2022.111505"},{"issue":"9","key":"e_1_2_8_25_1","doi-asserted-by":"crossref","DOI":"10.1063\/5.0060697","article-title":"Stiff Neural Ordinary Differential Equations","volume":"31","author":"Kim S.","year":"2021","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"key":"e_1_2_8_26_1","unstructured":"A.Gholami K.Keutzer andG.Biros \u201cANODE: Unconditionally Accurate Memory\u2010Efficient Gradients for Neural ODEs \u201d arXiv Preprint arXiv:1902.10298 (2019)."},{"key":"e_1_2_8_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVT.2011.2106527"},{"key":"e_1_2_8_28_1","doi-asserted-by":"crossref","unstructured":"M.Kim J.Schaeffer M. 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