3 papers
math.PR2026
Critical tensor covariance at the Marchenko-Pastur threshold
Xiaohui Xie
For a centered, variance-one random variable with finite fourth moment, let be the vector of square-free degree- monomials in independent copies of . At the criti…
cs.LG2025
Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie +1
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while prese…
cs.LG2024
BiLO: Bilevel Local Operator Learning for PDE Inverse Problems
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie +1
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization…