{"id":5277,"date":"2021-03-12T13:39:19","date_gmt":"2021-03-12T12:39:19","guid":{"rendered":"https:\/\/www.mi.uni-koeln.de\/NumSim\/?p=5277"},"modified":"2021-03-12T13:39:19","modified_gmt":"2021-03-12T12:39:19","slug":"talk-on-2021-03-18-a-tour-of-bifurcationkit-and-some-results-on-mean-fields-of-spiking-neurons","status":"publish","type":"post","link":"https:\/\/www.mi.uni-koeln.de\/NumSim\/2021\/03\/12\/talk-on-2021-03-18-a-tour-of-bifurcationkit-and-some-results-on-mean-fields-of-spiking-neurons\/","title":{"rendered":"Talk on 2021-03-18: A tour of BifurcationKit and some results on mean fields of spiking neurons"},"content":{"rendered":"\n<p><em>Speaker<\/em>: <strong>Dr. Romain Veltz<\/strong>, <a rel=\"noreferrer noopener\" aria-label=\"INRIA (opens in a new tab)\" href=\"http:\/\/romainveltz.pythonanywhere.com\/\" target=\"_blank\">INRIA<\/a>, France<br><em>Date: <\/em><strong>Thursday, 18th March 2021, 10am (CET)<\/strong><br><em>Zoom-Link:<\/em> Please request via email from <a href=\"https:\/\/www.mi.uni-koeln.de\/NumSim\/schlottke-lakemper\/\">Michael Schlottke-Lakemper<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Abstract<\/h2>\n\n\n\n<p>In this talk, I will first present the basics of bifurcation theory. Then, I will give a panorama of\u00a0<code><a href=\"https:\/\/github.com\/rveltz\/BifurcationKit.jl\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"BifurcationKit.jl (opens in a new tab)\">BifurcationKit.jl<\/a><\/code>, a Julia package to perform numerical bifurcation analysis of large dimensional equations (PDE, nonlocal equations, etc) possibly on GPUs using Matrix-Free \/ Sparse Matrix formulations of the problem. Julia programming language gives access to a rich ecosystem (PDE, GPU, AD, cluster&#8230;). Notably, numerical bifurcation analysis can be done\u00a0<strong>entirely<\/strong>\u00a0on GPU as will be shown in an example.<\/p>\n\n\n\n<p><code>BifurcationKit<\/code>\u00a0incorporates continuation algorithms (PALC, deflated continuation, &#8230;) which can be used to perform fully automatic bifurcation diagram computation of stationary states. I will showcase this with the 2d Bratu problem.<\/p>\n\n\n\n<p>Additionally, by leveraging on the above methods, the package can also seek for periodic orbits of Cauchy problems by casting them into an equation of high dimension. It is by now, one of the only software which provides parallel (Standard \/ Poincar\u00e9) shooting methods and finite differences based methods to compute periodic orbits in high dimensions. I will present an application highlighting the ability to fine tune\u00a0<code>BifurcationKit<\/code>\u00a0to get performance.<\/p>\n\n\n\n<p>In a last part, I will describe a mean field model of stochastic spiking neurons described with a 2d measure valued equation. I will present a numerical scheme based on an implicit Finite Volume method. I will then provide some mathematical properties of the mean field concerning well posedness and stationary solutions. Additionally, I will show how\u00a0<code>BifurcationKit.jl<\/code>\u00a0can be used to study numerically the model. Finally, I will conclude on open problems, some of which could hopefully be tackled numerically with\u00a0<code><a href=\"https:\/\/github.com\/trixi-framework\/Trixi.jl\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"Trixi.jl (opens in a new tab)\">Trixi.jl<\/a><\/code>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: Dr. Romain Veltz, INRIA, FranceDate: Thursday, 18th March 2021, 10am (CET)Zoom-Link: Please request via email from Michael Schlottke-Lakemper Abstract In this talk, I will first present the basics of bifurcation theory. Then, I will give a panorama of\u00a0BifurcationKit.jl, a &hellip; <a href=\"https:\/\/www.mi.uni-koeln.de\/NumSim\/2021\/03\/12\/talk-on-2021-03-18-a-tour-of-bifurcationkit-and-some-results-on-mean-fields-of-spiking-neurons\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,41],"tags":[],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/posts\/5277"}],"collection":[{"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/comments?post=5277"}],"version-history":[{"count":2,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/posts\/5277\/revisions"}],"predecessor-version":[{"id":5279,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/posts\/5277\/revisions\/5279"}],"wp:attachment":[{"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/media?parent=5277"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/categories?post=5277"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/tags?post=5277"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}