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math.NA2021
A Novel Randomized XR-Based Preconditioned CholeskyQR Algorithm
Yuwei Fan, Yixiao Guo, Ting Lin
CholeskyQR is a simple and fast QR decomposition via Cholesky decomposition, while it has been considered highly sensitive to the condition number. In this paper, we provide a rand…
math.NA2021
Multi-Level Fine-Tuning: Closing Generalization Gaps in Approximation of Solution Maps under a Limited Budget for Training Data
Zhihan Li, Yuwei Fan, Lexing Ying
In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schrödinger equation). In this pape…