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<b><i>"Solving PDEs: From Neural Single Operator to Neural Multi-Operator Foundation Models"</i></b></div>
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<b>Zecheng Zhang</b></div>
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Assistant Professor,</div>
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Department of Mathematics,</div>
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Florida State University </div>
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Please feel free to forward/share this invitation with other groups/disciplines that might be interested in this talk/topic.
<b>All are welcome to attend. </b></div>
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NOTE: <b>In-person attendance is requested.</b> Zoom access is intended for external (non-departmental) participants only. </div>
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<b>https://fsu.zoom.us/j/94273595552 </b></div>
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Meeting # <b>942 7359 5552 </b></div>
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🎦 Colloquium recordings will be made available here, <a href="https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.sc.fsu.edu%2Fcolloquium&data=05%7C02%7Csc-seminar-announce%40lists.fsu.edu%7Cbdb767fab9a24904c68608dce3f412b0%7Ca36450ebdb0642a78d1b026719f701e3%7C0%7C0%7C638635884619139111%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=renjmgakWTbTQ7tx8%2BlOU1et78%2FiwRo%2FqGAviePS1vM%3D&reserved=0" originalsrc="https://www.sc.fsu.edu/colloquium" shash="JquO3NbK5r3tZ1YXokkTEROCxFjA4d+GqYzf+XmhIW/t+ih83UGk+Trcp2eQ2Yxaw6d3j0PU2/Dma/Wu7ixyPiaFM16nh3OYYeyDw8dmFLYY6QhjYEEPoPa0Rl9rJGl6H6AQuV2fTITMDpRL/USemdYlTcRTXTUbHTC2yv1FXps=">
https://www.sc.fsu.edu/colloquium</a> </div>
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<b>Wednesday, Oct 9th, 2024, Schedule: </b></div>
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* 3:00 to 3:30 PM Eastern Time (US and Canada) </div>
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☕ Nespresso & Teatime - 417 DSL Commons </div>
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<b>* 3:30 to 4:30 PM Eastern Time (US and Canada) </b></div>
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<b>🕟 Colloquium - 499 DSL Seminar Room </b></div>
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<b>Abstract: </b></div>
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In this talk, I will explore the machine learning approach to solving complex physical systems modeled by partial differential equations (PDEs). Since many PDE-solving problems can be framed as operator approximations, we will focus on operator learning. The
discussion will begin by extending the universal approximation theorem to make it invariant to discretization, followed by an examination of distributed algorithms that can further improve the network flexibility to handle complex multiscale problems. To improve
the network's ability to extrapolate, we will delve into multi-operator learning, particularly in designing foundation models that can address previously unseen problems. To mathematically quantify of these approximations, the talk will conclude with a discussion
of neural scaling laws, focusing on the convergence of operator learning networks and the analysis of generalization error.</div>
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<b>Additional colloquium details can be found here, </b></div>
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<a href="https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.sc.fsu.edu%2Fnews-and-events%2Fcolloquium%2F1819-colloquium-with-zecheng-zhang-2024-10-09&data=05%7C02%7Csc-seminar-announce%40lists.fsu.edu%7Cbdb767fab9a24904c68608dce3f412b0%7Ca36450ebdb0642a78d1b026719f701e3%7C0%7C0%7C638635884619139111%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=MrMVs%2Bx5q%2FYixuIA9XIDSCf2quPqmnVuemJ%2FLjLWFbk%3D&reserved=0" originalsrc="https://www.sc.fsu.edu/news-and-events/colloquium/1819-colloquium-with-zecheng-zhang-2024-10-09" shash="CB96rxvBv5uXg5KBVAjp3VP3yDMIezIaBUq/bpPhsQgen4EC/7yI+r//uZLcH6kvPffEs6A5GSJjrJWnIvx0zbG+WdFjoNDABsY/UzvfR9UCfOx8gMdms7NqVdGM+hgxn/SBDUci4nfoJkBBEpBYG3aHQlLxDXOFg4/FCiGV5F0=">https://www.sc.fsu.edu/news-and-events/colloquium/1819-colloquium-with-zecheng-zhang-2024-10-09</a></div>
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