{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T08:09:42Z","timestamp":1775117382115,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T00:00:00Z","timestamp":1771632000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T00:00:00Z","timestamp":1771632000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["2023YFA1009300"],"award-info":[{"award-number":["2023YFA1009300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12531014"],"award-info":[{"award-number":["12531014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271107"],"award-info":[{"award-number":["12271107"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171039"],"award-info":[{"award-number":["12171039"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1007\/s10915-026-03195-x","type":"journal-article","created":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T06:35:59Z","timestamp":1771655759000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Acceleration via Perturbations on Low-resolution Ordinary Differential Equations"],"prefix":"10.1007","volume":"107","author":[{"given":"Xudong","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingqi","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,21]]},"reference":[{"key":"3195_CR1","doi-asserted-by":"publisher","first-page":"1102","DOI":"10.1137\/S0363012998335802","volume":"38","author":"F Alvarez","year":"2000","unstructured":"Alvarez, F.: On the minimizing property of a second order dissipative system in Hilbert spaces. SIAM J. Control. Optim. 38, 1102\u20131119 (2000)","journal-title":"SIAM J. Control. Optim."},{"key":"3195_CR2","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1016\/S0021-7824(01)01253-3","volume":"81","author":"F Alvarez","year":"2002","unstructured":"Alvarez, F., Attouch, H., Bolte, J., Redont, P.: A second-order gradient-like dissipative dynamical system with Hessian-driven damping: Application to optimization and mechanics. J. Math. Pures Appl. 81, 747\u2013779 (2002)","journal-title":"J. Math. Pures Appl."},{"key":"3195_CR3","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s10107-020-01591-1","volume":"193","author":"H Attouch","year":"2022","unstructured":"Attouch, H., Chbani, Z., Fadili, J., Riahi, H.: First-order optimization algorithms via inertial systems with Hessian driven damping. Math. Program. 193, 113\u2013155 (2022)","journal-title":"Math. Program."},{"key":"3195_CR4","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1137\/130910294","volume":"24","author":"H Attouch","year":"2014","unstructured":"Attouch, H., Peypouquet, J., Redont, P.: A dynamical approach to an inertial forward-backward algorithm for convex minimization. SIAM J. Optim. 24, 232\u2013256 (2014)","journal-title":"SIAM J. Optim."},{"key":"3195_CR5","unstructured":"Betancourt, M., Jordan, M.I., Wilson, A.C.: On symplectic optimization. arXiv preprint arXiv:1802.03653 (2018)"},{"key":"3195_CR6","unstructured":"Chen, S., Shi, B., Yuan, Y.-X.: Gradient norm minimization of Nesterov acceleration: $$o(1\/k^3)$$. arXiv preprint arXiv:2209.08862 (2022)"},{"key":"3195_CR7","first-page":"743","volume":"6","author":"S Fiori","year":"2005","unstructured":"Fiori, S.: Quasi-geodesic neural learning algorithms over the orthogonal group: A tutorial. J. Mach. Learn. Res. 6, 743\u2013781 (2005)","journal-title":"J. Mach. Learn. Res."},{"key":"3195_CR8","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/abf5d4","volume":"2021","author":"G Fran\u00e7a","year":"2021","unstructured":"Fran\u00e7a, G., Jordan, M.I., Vidal, R.: On dissipative symplectic integration with applications to gradient-based optimization. J. Stat. Mech: Theory Exp. 2021, 043402 (2021)","journal-title":"J. Stat. Mech: Theory Exp."},{"key":"3195_CR9","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1109\/JPROC.1996.503147","volume":"84","author":"U Helmke","year":"1996","unstructured":"Helmke, U., Moore, J.: Optimization and dynamical systems. Proc. IEEE 84, 907 (1996)","journal-title":"Proc. IEEE"},{"key":"3195_CR10","doi-asserted-by":"crossref","unstructured":"Jordan, M.I.: Dynamical, symplectic and stochastic perspectives on gradient-based optimization, Proceedings of the International Congress of Mathematicians (ICM 2018), pp.\u00a0523\u2013549 (2019)","DOI":"10.1142\/9789813272880_0022"},{"key":"3195_CR11","unstructured":"Juditsky, A.: Convex Optimization II: Algorithms. Lecture notes, (2013)"},{"key":"3195_CR12","unstructured":"Krichene, W., Bayen, A., Bartlett, P.L.: Accelerated mirror descent in continuous and discrete time, in Advances in Neural Information Processing Systems, vol.\u00a028, (2015)"},{"key":"3195_CR13","doi-asserted-by":"crossref","unstructured":"Li, B., Shi, B., Yuan, Y.-X.: Proximal subgradient norm minimization of ISTA and FISTA. Appl. Comput. Harmon. Anal., 101848 (2025)","DOI":"10.1016\/j.acha.2025.101848"},{"key":"3195_CR14","doi-asserted-by":"publisher","first-page":"2150","DOI":"10.1137\/23M158111X","volume":"34","author":"B Li","year":"2024","unstructured":"Li, B., Shi, B., Yuan, Y.-X.: Linear convergence of forward-backward accelerated algorithms without knowledge of the modulus of strong convexity. SIAM J. Optim. 34, 2150\u20132168 (2024)","journal-title":"SIAM J. Optim."},{"key":"3195_CR15","unstructured":"Nesterov, Y.: A method for solving the convex programming problem with convergence rate $${O}(1\/k^2)$$, Proceedings of the USSR Academy of Sciences, 269, pp.\u00a0543\u2013547 (1983)"},{"key":"3195_CR16","doi-asserted-by":"crossref","unstructured":"Nesterov, Y.: Lectures on Convex Optimization, Springer, (2018)","DOI":"10.1007\/978-3-319-91578-4"},{"key":"3195_CR17","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1080\/01630560008816971","volume":"21","author":"J Schropp","year":"2000","unstructured":"Schropp, J., Singer, I.: A dynamical systems approach to constrained minimization. Numer. Funct. Anal. Optim. 21, 537\u2013551 (2000)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"3195_CR18","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s10107-021-01681-8","volume":"195","author":"B Shi","year":"2022","unstructured":"Shi, B., Du, S.S., Jordan, M.I., Su, W.J.: Understanding the acceleration phenomenon via high-resolution differential equations. Math. Program. 195, 79\u2013148 (2022)","journal-title":"Math. Program."},{"key":"3195_CR19","unstructured":"Shi, B., Du, S.S., Su, W., Jordan, M.I.: Acceleration via symplectic discretization of high-resolution differential equations, in Advances in Neural Information Processing Systems, vol.\u00a032, (2019)"},{"key":"3195_CR20","first-page":"1","volume":"17","author":"W Su","year":"2016","unstructured":"Su, W., Boyd, S., Cand\u00e8s, E.J.: A differential equation for modeling Nesterov\u2019s accelerated gradient method: Theory and insights. J. Mach. Learn. Res. 17, 1\u201343 (2016)","journal-title":"J. Mach. Learn. Res."},{"key":"3195_CR21","doi-asserted-by":"publisher","first-page":"E7351","DOI":"10.1073\/pnas.1614734113","volume":"113","author":"A Wibisono","year":"2016","unstructured":"Wibisono, A., Wilson, A.C., Jordan, M.I.: A variational perspective on accelerated methods in optimization. Proc. Natl. Acad. Sci. 113, E7351\u2013E7358 (2016)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"3195_CR22","first-page":"1","volume":"22","author":"AC Wilson","year":"2021","unstructured":"Wilson, A.C., Recht, B., Jordan, M.I.: A Lyapunov analysis of accelerated methods in optimization. J. Mach. Learn. Res. 22, 1\u201334 (2021)","journal-title":"J. Mach. Learn. Res."},{"key":"3195_CR23","unstructured":"Yang, L., Arora, R., braverman, V., Zhao, T.: The physical systems behind optimization algorithms, in Advances in Neural Information Processing Systems, vol.\u00a031, (2018)"},{"key":"3195_CR24","unstructured":"Zhang, J., Mokhtari, A., Sra, S., Jadbabaie, A.: Direct Runge-Kutta discretization achieves acceleration, in Advances in Neural Information Processing Systems, vol.\u00a031, (2018)"},{"key":"3195_CR25","unstructured":"Zhang, P., Orvieto, A., Daneshmand, H., Hofmann, T., Smith, R.S.: Revisiting the role of Euler numerical integration on acceleration and stability in convex optimization, in Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, vol.\u00a0130, PMLR, pp.\u00a03979\u20133987 (2021)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03195-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-026-03195-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03195-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T07:32:01Z","timestamp":1775115121000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-026-03195-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,21]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["3195"],"URL":"https:\/\/doi.org\/10.1007\/s10915-026-03195-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,21]]},"assertion":[{"value":"2 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}}],"article-number":"7"}}