From the 2 of 16 linked papers with an AI index.
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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 interdisciplinary field that integrates machine learning with scientific computing. By mapping infinite-dimensional function spaces, this approach…
fOGA: An Orthogonal Greedy Algorithm for Fractional Laplacian Problems
Ruitong Shan, Young Ju Lee, Jiwei Jia
In this paper, we propose a numerical method for fractional Laplace equations that combines finite difference discretization with shallow neural network approximation. The fraction…
Neural Preconditioned Born Series: A Metric-Matched Framework for Learning-based Preconditioners
Juntao Wang, Jiwei Jia, Xinliang Liu
High-frequency Helmholtz problems in heterogeneous media remain challenging for both classical iterative methods and end-to-end neural PDE solvers. We propose Neural Preconditioned…