6 papers · 2 filters
ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems
Zheng Lu, Jiwei Jia, Young Ju Lee
Inverse problems governed by partial differential equations are difficult when observations are sparse and the unknown coefficient field contains both large- and small-scale struct…
McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation
Jiwei Jia, Xinliang Liu, Juntao Wang +1
Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coar…
Second-Order Area/Volume-Preserving PFEMs for Surface Diffusion via Simpson--Boole Geometric Identities
Zhiqing Pan, Jiwei Jia, Lian Zhang
We propose second-order-in-time parametric finite element methods for surface diffusion of closed curves in two dimensions and closed surfaces in three dimensions. The construction…
Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems
Kuilin Qin, Lianfang Wang, Xu Sun +4
Operator learning is an emerging field at the intersection of machine learning and scientific computing. By learning mappings between function spaces, neural operators provide data…
Boundary neuron method for solving partial differential equations
Ye Lin, Wentao Liu, Young Ju Lee +1
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow net…
Born-Preconditioned Learning for Iterative Neural PDE Solvers
Juntao Wang, Jiwei Jia, Xinliang Liu
Simulating high-frequency waves in spatially varying media remains challenging for both classical iterative methods and neural PDE solvers. We propose Neural Preconditioned Born Se…