【專題演講】2026-03-23 11:00-12:00 Hypercircle-Based Optimization for Physics-Informed Neural Networks in Boundary Value Problems 劉雪峰 (東京女子大学数理科学科)
數學跨領域研究中心 2026年專題演講
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DATE |
2026-03-23 11:00-12:00 |
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PLACE |
數學系館 31106 教室 |
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SPEAKER |
劉雪峰 (刘雪峰）/ Xuefeng LIU 東京女子大学 現代教養学部 数理科学科 |
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TITLE |
Hypercircle-Based Optimization for Physics-Informed Neural Networks in Boundary Value Problems |
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ABESTRACT |
Physics-Informed Neural Networks (PINNs) have recently attracted significant attention as a mesh-free approach for solving partial differential equations. However, a common drawback of PINNs is the difficulty in obtaining high-precision solutions and in providing rigorous error estimation. In this talk, we introduce a new framework that combines the PINN methodology with the hypercircle method for solving boundary value problems. The proposed approach formulates an optimization problem based on a hypercircle-type residual norm defined on two approximation spaces: one in $H^1(\Omega)$ and the other in $H(\mathrm{div})$. A key feature of this formulation is that it enables the direct evaluation of error bounds for the obtained approximate solutions. Numerical experiments demonstrate the effectiveness of the proposed method for several model problems, including cases with limited solution regularity. At the end of the talk, we will briefly introduce the CES-Alpha system, a cloud-based platform designed for scientific computing and computational education. |
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SPONSOR |
國立成功大學數學跨領域研究中心 |