<div dir="ltr">Buongiorno a tutt*,<br><br>ricevo e inoltro il link zoom per l'ultima lezione del corso qui sotto<br><br>Cordiali saluti,<br>Lorenzo Tamellini<br><br><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>Da: <b class="gmail_sendername" dir="auto">francois murat</b> <span dir="auto"><<a href="mailto:francois.murat@sorbonne-universite.fr">francois.murat@sorbonne-universite.fr</a>></span><br>Date: gio 14 dic 2023 alle ore 02:10<br>Subject: [sciences-ljll-seminaire] Ce jeudi 14 décembre de 11h à 12h30 : Mini-cours-3 des Leçons Jacques-Louis Lions d'Andrew Stuart (exposé avec diffusion simultanée par Zoom)<br>To: <<a href="mailto:sciences-ljll-seminaire@listes.sorbonne-universite.fr">sciences-ljll-seminaire@listes.sorbonne-universite.fr</a>><br></div><br><br><div style="word-wrap:break-word;line-break:after-white-space"><div style="margin:0px;font-stretch:normal;line-height:normal;color:rgba(0,0,0,0.85)"><font face="HelveticaNeue"><b>Ce </b><span style="color:rgb(0,0,0)"><b>jeudi 14 décembre</b></span><b> de 11h à 12h30 : </b></font></div><div style="margin:0px;font-stretch:normal;line-height:normal;color:rgba(0,0,0,0.85)"><font face="HelveticaNeue"><b>Mini-cours-3 des Leçons Jacques-Louis Lions d'</b><span style="color:#000000"><b>Andrew Stuart </b></span></font></div><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue">(Institut de technologie de Californie (Caltech))</font></span></p><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><br></font></p><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal"><font face="HelveticaNeue"><span style="font-kerning:none"><b>Identifiants de connexion Zoom </b></span><span style="font-kerning:none;color:rgba(0,0,0,0.85)"><b>pour le Mini-cours-3 :</b></span></font></div><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><span style="font-kerning:none"></span><br></font></div><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue"><b>Date et heure : </b>Jeudi 14 décembre 2023 Mini-cours-3 11h00-12h30 (heure de Paris)</font></span></div><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue"><b>Sujet : </b>Mini-cours-3 Je 14 12 2023 A. Stuart</font></span></div><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><b><font face="HelveticaNeue">Lien Zoom pour assister à l'exposé :</font></b></span></div><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue"><a href="https://zoom.us/j/95710296184?pwd=eWZKVGdsRUZidFRwcHFtNGxqWEsyZz09" target="_blank">https://zoom.us/j/95710296184?pwd=eWZKVGdsRUZidFRwcHFtNGxqWEsyZz09</a></font></span></div><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue"><b>ID de réunion : </b>957 1029 6184</font></span></div><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue"><b>Code secret : </b>325479</font></span></div><div style="margin:0px;text-align:justify;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><span style="font-kerning:none"></span><br></font></div><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue"><b>Attention</b> : le lien Zoom sera différent chaque jour.</font></span></p><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal;min-height:17px"><font face="HelveticaNeue"><span style="font-kerning:none"><b></b></span><br></font></p><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><br></font></p><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal;color:rgba(0,0,0,0.85)"><span style="font-kerning:none"><font face="HelveticaNeue">Données par <b>Andrew Stuart </b> (Institut de technologie de Californie (Caltech))</font></span></p><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal;color:rgba(0,0,0,0.85)"><span style="font-kerning:none"><font face="HelveticaNeue">les <b>Leçons Jacques-Louis Lions 2023 </b>consisteront en : </font></span></p><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue"><b>— un mini-cours intitulé <br>
Ensemble Kalman filter : Algorithms, analysis and applications </b><br>
3 séances, les <b>mardi 12, mercredi 13 et jeudi 14 décembre</b> 2023 de 11h à 12h30, <br>
Salle du séminaire du Laboratoire Jacques-Louis Lions, <br>
barre 15-16, 3ème étage, salle 09 (15-16-3-09), <br>
Sorbonne Université, Campus Jussieu, 4 place Jussieu, Paris 5ème, </font></span></p><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><font face="HelveticaNeue"><b>— et un colloquium intitulé <br>
Operator learning : Acceleration and discovery of computational models </b><br>
le <b>vendredi 15 décembre</b> 2023 de 14h à 15h, <br>
Amphithéâtre 25, <br>
entrée face à la tour 25, niveau dalle Jussieu,<br>
Sorbonne Université, Campus Jussieu, 4 place Jussieu, Paris 5ème. </font></span></p><div style="margin:0px;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><span style="font-kerning:none"></span><br></font></div><p style="margin:0px 0px 4.4px;text-align:justify;font-stretch:normal;line-height:normal"><span style="font-kerning:none"><b><font face="HelveticaNeue">Tous les exposés seront donnés en présence et retransmis en temps réel par Zoom.</font></b></span></p><div style="margin:0px;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><br></font></div><div style="margin:0px;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><br></font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><span style="font-style:normal"><b><font face="HelveticaNeue">Résumé du mini-cours</font></b></span></div><div style="margin:0px;font-stretch:normal;line-height:normal"><span style="font-style:normal"><b><font face="HelveticaNeue">Ensemble Kalman Filter: Algorithms, analysis and applications</font></b></span></div><div style="margin:0px;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><br></font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">In 1960 Rudolph Kalman [1] published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of dynamical systems. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. Kalman's paper is confined to linear dynamical systems subject to Gaussian noise; the work of Geir Evensen [2] in 1994 opened up far wider applicability of Kalman's ideas by introducing the ensemble Kalman filter. </font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">The ensemble Kalman filter applies to the setting in which nonlinear and noisy observations are used to make improved predictions of the state of a Markov chain. The algorithm results in an interacting particle system combining elements of the Markov chain and the observation process. In these lectures I will introduce a unifying mean-field perspective on the algorithm, derived in the limit of an infinite number of interacting particles. I will then describe how the methodology can be used to study inverse problems, opening up diverse applications beyond prediction in dynamical systems. Finally I will describe analysis of the accuracy of the methodology, both in terms of accuracy and uncertainty quantification; despite its widespread adoption in applications, a complete mathematical theory is lacking and there are many opportunities for analysis in this area.</font></div><div style="margin:0px;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><br></font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">Lecture 1: The algorithm</font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">Lecture 2: Inverse problems and applications</font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">Lecture 3: Analysis of accuracy and uncertainty quantification</font></div><div style="margin:0px;font-stretch:normal;line-height:normal;min-height:16px"><font face="HelveticaNeue"><br></font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">[1] R. Kalman, {A new approach to linear filtering and prediction problems.}</font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">Journal of Basic Engineering, 82:35–45, 1960.</font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">[2] G. Evensen, {Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics.}</font></div><div style="margin:0px;font-stretch:normal;line-height:normal"><font face="HelveticaNeue">Journal of Geophysical Research: Oceans, 99(C5):10143–10162, 1994.</font></div><div><b style="text-align:justify;padding:0px;margin:0px"><font face="HelveticaNeue"><br></font></b></div><div style="margin:0px;font-stretch:normal;line-height:normal;min-height:16px"><b style="font-style:normal"><font face="HelveticaNeue"><br></font></b></div><div><b style="font-style:normal"><font face="HelveticaNeue"><span style="text-align:justify;padding:0px;margin:0px">Références biblio</span><span style="text-align:justify;padding:0px;margin:0px">graphiques pour le</span><span style="text-align:justify;padding:0px;margin:0px">s Leçons Jacques-Louis Lions 2023 (Andrew Stuart)</span></font></b></div><div><span style="text-align:justify;padding:0px;margin:0px"><span style="text-align:start;font-style:normal"><font face="HelveticaNeue"><a href="https://www.ljll.math.upmc.fr/IMG/pdf/references_biblio_lecons_jacques-louis_lions_2023_andrew_stuart.pdf" target="_blank">https://www.ljll.math.upmc.fr/IMG/pdf/references_biblio_lecons_jacques-louis_lions_2023_andrew_stuart.pdf</a></font></span></span></div><div><span style="text-align:justify;padding:0px;margin:0px;font-style:normal"><font face="HelveticaNeue"><br></font></span></div><div><br></div></div></div></div>