10 papers
Penalty-Free Natural Deep Ritz Method Based on de Rham Complex for High-Dimensional Dirichlet Boundary Value Problems
Jiarong Chen, Xia Ji, Haijun Yu +1
Deep neural networks show great promise for high-dimensional PDEs, yet enforcing essential boundary conditions remains challenging, especially as penalty parameters require problem…
Efficient Image-to-Image Schrödinger Bridge for CT Field of View Extension
Zhenhao Li, Song Ni, Long Yang +6
Computed tomography (CT) is a cornerstone imaging modality for non-invasive, high-resolution visualization of internal anatomical structures. However, when the scanned object excee…
A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation
Xinwei Hu, Jingrun Chen, Haijun Yu
The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical met…
Predictive Moving Sample Method for Physics-Informed Neural Solvers of Time-Dependent PDEs
Beining Xu, Bocheng Zhang, Haijun Yu +2
Time-dependent partial differential equations (PDEs) often develop sharp fronts, localized peaks, and other moving structures that occupy only a small portion of the space--time do…
An Efficient Stochastic Subgradient Method for the Global Placement Problem in Very Large-Scale Integration Circuits
Yi-Shuang Yue, Yu-Hong Dai, Haijun Yu
The placement problem in Very Large-Scale Integration (VLSI) circuits is a critical step in chip design. Its primary goal is to optimize the wirelength of circuit components within…
Fast Jacobi Spectral Methods and Closure Approximations for the Homogeneous FENE Model of Complex Fluids
Runkai Feng, Jie Shen, Haijun Yu
The Finitely Extensible Nonlinear Elastic (FENE) dumbbell model is a widely used mathematical model for complex fluids. Direct simulation of the FENE Fokker--Planck equation is com…