| 國（境）外文教專家系列講座一百七十五講-趙雁翔：Supervised Optimal Transport |
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一、主講人介紹：趙雁翔教授 趙雁翔教授，2002年于大連理工大學應用數學系獲得理學學士，2005年于大連理工大學應用數學系獲得理學碩士專業，2011年于賓州州立大學獲得數學博士學位。2011-2014年于加州大學圣地亞哥分校從事博士后工作。2014年至今于喬治華盛頓大學數學系工作。趙雁翔主要從事生物數學建模和計算數學的研究，論文發表在PRL, PNAS, SIAM Applied Math, JCP等頂級期刊上。
二、講座信息 Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan which traditional optimal transport cannot enforce. Here we introduce Supervised Optimal Transport (sOT) that formulates a constrained optimal transport problem where couplings between certain elements are prohibited according to specific applications. sOT is proved to be equivalent to an penalized optimization problem, from which efficient algorithms are designed to solve its entropy regularized formulation. We demonstrate the capability of sOT by comparing it to other variants and extensions of traditional OT in color transfer problem. We also study the barycenter problem in sOT formulation, where we discover and prove a unique reverse and portion selection (control) mechanism. Supervised optimal transport is broadly applicable to applications in which constrained transport plan is involved and the original unit should be preserved by avoiding normalization. 時間：2023年6月14日10:00-11:00 地點：數學院424會議室
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中國海洋大學國際合作與交流處 數學科學學院
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