【115/3/23】11:00-12:00 Prof. Xuefeng LIU(Department of Mathematical Sciences, School of Contemporary Liberal Arts, Tokyo Woman’s Christian University)
| Special Lecture of the IRCM | |
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| Time | 2026-3-23 11:00-12:00 |
| Venue | 31106, Department of Mathematics |
| Speaker | Prof. Xuefeng LIU(Department of Mathematical Sciences, School of Contemporary Liberal Arts, Tokyo Woman’s Christian University) |
| Title | Hypercircle-Based Optimization for Physics-Informed Neural Networks in Boundary Value Problems |
| Abstract | 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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