{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:27:57Z","timestamp":1787232477980,"version":"3.56.0"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2021YFA1001200"],"award-info":[{"award-number":["2021YFA1001200"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2020YFA0712000"],"award-info":[{"award-number":["2020YFA0712000"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12031013"],"award-info":[{"award-number":["12031013"]}],"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":["12171013"],"award-info":[{"award-number":["12171013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2024,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The noisy leaky integrate-and-fire (NLIF) model describes the voltage configurations of neuron networks with an interacting many-particles system at a microscopic level. When simulating neuron networks of large sizes, computing a coarse-grained mean-field Fokker\u2013Planck equation solving the voltage densities of the networks at a macroscopic level practically serves as a feasible alternative in its high efficiency and credible accuracy when the interaction within the network remains relatively low. However, the macroscopic model fails to yield valid results of the networks when simulating considerably synchronous networks with active firing events. In this paper, we propose a multiscale solver for the NLIF networks, inheriting the macroscopic solver\u2019s low cost and the microscopic solver\u2019s high reliability. For each temporal step, the multiscale solver uses the macroscopic solver when the firing rate of the simulated network is low, while it switches to the microscopic solver when the firing rate tends to blow up. Moreover, the macroscopic and microscopic solvers are integrated with a high-precision switching algorithm to ensure the accuracy of the multiscale solver. The validity of the multiscale solver is analyzed from two perspectives: first, we provide practically sufficient conditions that guarantee the mean-field approximation of the macroscopic model and present rigorous numerical analysis on simulation errors when coupling the two solvers; second, the numerical performance of the multiscale solver is validated through simulating several large neuron networks, including networks with either instantaneous or periodic input currents which prompt active firing events over some time.<\/jats:p>","DOI":"10.1137\/23m1573276","type":"journal-article","created":{"date-parts":[[2024,3,19]],"date-time":"2024-03-19T04:45:58Z","timestamp":1710823558000},"page":"561-587","source":"Crossref","is-referenced-by-count":3,"title":["A Synchronization-Capturing Multiscale Solver to the Noisy Integrate-and-Fire Neuron Networks"],"prefix":"10.1137","volume":"22","author":[{"given":"Ziyu","family":"Du","sequence":"first","affiliation":[{"name":"The Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yantong","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mathematics Science, Peking University, Beijing, 100871, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4822-0275","authenticated-orcid":true,"given":"Zhennan","family":"Zhou","sequence":"additional","affiliation":[{"name":"Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,3,19]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/7.3.237"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008925309027"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1162\/089976699300016179"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1186\/2190-8567-1-7"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.10.027"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"M. J. C\u00e1ceres and A. Ramos-Lora, An Understanding of the Physical Solutions and the Blow-up Phenomenon for Nonlinear Noisy Leaky Integrate and Fire Neuronal Models, preprint, arXiv:2011.05860, 2020.","DOI":"10.4208\/cicp.OA-2020-0241"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2017024"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2018014"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2012.747536"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/28\/9\/3365"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1214\/14-AAP1044"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2015.01.007"},{"key":"ref13","unstructured":"X. Dou and Z. Zhou, Dilating Blow-up Time: A Generalized Solution of the NNLIF Neuron Model and Its Global Well-Posedness, preprint, arXiv:2206.06972, 2022."},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/21M1445600"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110195"},{"key":"ref16","first-page":"620","volume":"9","author":"Lapicque L.","year":"1907","journal-title":"J. Physiol. Pathol. Gen."},{"key":"ref17","unstructured":"L. Le and Y. Li, Supervised Parameter Estimation of Neuron Populations from Multiple Firing Events, preprint, arXiv:2210.01767, 2022."},{"key":"ref18","volume":"1","author":"Liu J.-G.","year":"2021","journal-title":"Math. Neurosci. Appl."},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/20M1338368"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-008-0117-3"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-012-0429-1"},{"key":"ref22","first-page":"431","volume-title":"Computational Neuroscience: A Comprehensive Approach","author":"Renart A.","year":"2004"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2021025"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1007265"},{"key":"ref25","volume-title":"Introduction to Theoretical Neurobiology: Linear Cable Theory and Dendritic Structure","author":"Tuckwell H. C.","year":"1988"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-019-00712-w"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-013-0488-y"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/23M1573276","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:57:42Z","timestamp":1787230662000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1573276"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,19]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3,31]]}},"alternative-id":["10.1137\/23M1573276"],"URL":"https:\/\/doi.org\/10.1137\/23m1573276","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,19]]}}}