{"693297":{"#nid":"693297","#data":{"type":"event","title":"PhD Defense by Sebasti\u00e1n Guti\u00e9rrez Hern\u00e1ndez.","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETitle:\u003C\/strong\u003E \u2018Learning and optimizing paths between probability distributions. From action minimization to boundary-valued Hamiltonian flows\u2019.\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EDate:\u003C\/strong\u003E\u0026nbsp; November 4th\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ETime:\u003C\/strong\u003E\u0026nbsp;9.00am (EST)\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ERoom:\u0026nbsp;\u003C\/strong\u003E006\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EZoom link:\u0026nbsp;\u003C\/strong\u003E\u003Ca href=\u0022https:\/\/nam12.safelinks.protection.outlook.com\/?url=https%3A%2F%2Fgatech.zoom.us%2Fj%2F91925737499\u0026amp;data=05%7C02%7Cannouncements%40grad.gatech.edu%7C965bf546d6bd47800c1708df291cecaf%7C482198bbae7b4b258b7a6d7f32faa083%7C1%7C0%7C639274876397334306%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C\u0026amp;sdata=Fa%2FOCQj2JEjSW2gMYk5fxI8TOz9AKd9IKwHyhcTTtOs%3D\u0026amp;reserved=0\u0022\u003E\u003Cstrong\u003Ehttps:\/\/gatech.zoom.us\/j\/91925737499\u003C\/strong\u003E\u003C\/a\u003E\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ECommittee members\u003C\/strong\u003E:\u003C\/p\u003E\u003Cp\u003EDr. Haomin Zhou (Advisor)\u003C\/p\u003E\u003Cp\u003EDr. Peng Chen (Co-advisor)\u003C\/p\u003E\u003Cp\u003EDr. Sung Ha Kang\u003C\/p\u003E\u003Cp\u003EDr. Luca Dieci\u003C\/p\u003E\u003Cp\u003EDr. Shu Liu\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EFinding a path between two probability distributions is a recurring problem in optimal transport, generative modeling, population dynamics, and control. A broad class of these problems can be formulated through an action functional defined over curves of probability distributions. The corresponding first-order optimality conditions lead to a coupled Hamilton\u2013Jacobi and continuity system, which can be written as a boundary-value Hamiltonian flow in density space.\u003C\/p\u003E\u003Cp\u003EWe take three approaches for learning and optimizing them: Hamiltonian Rectification (HR), Neural Multiple Shooting (NMS), and Parametric Density Path Optimization (PDPO). In the talk, we are going to focus on Neural Multiple Shooting.\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EThe central idea of NMS is to reformulate the boundary-value problem in density space as a multiple-shooting problem in particle space. Since the particle dynamics are determined by the prescribed Hamiltonian system once the momentum is specified, the unknowns reduce to momentum maps that initialize a sequence of Hamiltonian initial-value problems. The resulting hybrid method combines neural approximation with classical multiple shooting: neural networks determine the momentum at the beginning of each shooting segment, while an ODE solver propagates the corresponding trajectories according to the prescribed dynamics.\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E","summary":"","format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003ELearning and optimizing paths between probability distributions. From action minimization to boundary-valued Hamiltonian flows\u2019\u003C\/p\u003E","format":"limited_html"}],"field_summary_sentence":[{"value":"Learning and optimizing paths between probability distributions. From action minimization to boundary-valued Hamiltonian flows\u2019"}],"uid":"27707","created_gmt":"2026-10-19 15:48:42","changed_gmt":"2026-10-19 15:49:55","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2026-11-04T09:00:20-05:00","event_time_end":"2026-11-04T11:00:00-05:00","event_time_end_last":"2026-11-04T11:00:00-05:00","gmt_time_start":"2026-11-04 14:00:20","gmt_time_end":"2026-11-04 16:00:00","gmt_time_end_last":"2026-11-04 16:00:00","rrule":null,"timezone":"America\/New_York"},"location":"Skiles room 006. ","extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78771","name":"Public"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}