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In our algorithm, we use frozen Gaussian approximation to approximate the wave function as a wave packet in integral form. The desired reduced density operator is then written as a Dyson series, which is the series expression of path integrals in quantum mechanics of interacting systems. To compute the Dyson series, we further approximate each term in the series using Gaussian wave packets, and then employ the idea of the inchworm method to accelerate the convergence of the series. The inchworm method formulates the series as an integro-differential equation of \u201cfull propagators&apos;&apos;, and rewrites the infinite series on the right-hand side using these full propagators, so that the number of terms in the sum can be significantly reduced, and faster convergence can be achieved. The performance of our algorithm is verified numerically by various experiments.<\/jats:p>","DOI":"10.22331\/q-2025-03-24-1667","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T16:09:13Z","timestamp":1742832553000},"page":"1667","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7890-2758","authenticated-orcid":false,"given":"Geshuo","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6651-6224","authenticated-orcid":false,"given":"Siyao","family":"Yang","sequence":"additional","affiliation":[{"name":"Committee on Computational and Applied Mathematics, Department of Statistics, University of Chicago, Chicago, IL 60637 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7086-7983","authenticated-orcid":false,"given":"Zhenning","family":"Cai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National University of Singapore, Singapore 119076"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,3,24]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Claude Leforestier, RH Bisseling, Charly Cerjan, MD Feit, Rich Friesner, A Guldberg, A Hammerich, G Jolicard, W Karrlein, H-D Meyer, et al. ``A comparison of different propagation schemes for the time dependent Schr\u00f6dinger equation''. 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