3 papers
math.NA2026
Preconditioned Truncated Single-Sample Estimators for Scalable Stochastic Optimization
Tianshi Xu, Difeng Cai, Hua Huang +2
Many large-scale stochastic optimization algorithms involve repeated solutions of linear systems or evaluations of log-determinants. In these regimes, computing exact solutions is…
math.NA2025
Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations
Difeng Cai, Paulina Sepúlveda
The appearance of singularities in the function of interest constitutes a fundamental challenge in scientific computing. It can significantly undermine the effectiveness of numeric…
stat.ML2025
Posterior Covariance Structures in Gaussian Processes
Difeng Cai, Edmond Chow, Yuanzhe Xi
In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is ba…