11 citations · 27 across the 22 of their papers we have counts for
5 papers · 1 filter
Physics-Informed Inference Time Scaling for Solving High-Dimensional PDE via Defect Correction
Zexi Fan, Yan Sun, Shihao Yang +1
Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We int…
What is a Sketch-and-Precondition Derivation for Low-Rank Approximation? Inverse Power Error or Inverse Power Estimation?
Ruihan Xu, Yiping Lu
Randomized sketching accelerates large-scale numerical linear algebra by reducing computational complexity. While the traditional sketch-and-solve approach reduces the problem size…
Randomized Iterative Solver as Iterative Refinement: A Simple Fix Towards Backward Stability
Ruihan Xu, Yiping Lu
Iterative sketching and sketch-and-precondition are well-established randomized algorithms for solving large-scale, over-determined linear least-squares problems. In this paper, we…
Which Spaces can be Embedded in -type Reproducing Kernel Banach Space? A Characterization via Metric Entropy
Yiping Lu, Daozhe Lin, Qiang Du
In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces. Metric entr…
Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality
Yiping Lu, Haoxuan Chen, Jianfeng Lu +2
In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method…