34 citations · 212 across the 40 of their papers we have counts for
4 papers · 1 filter
Feature Learning for the High Dimensional Stationary Schödinger Equation with Deep Ritz Method
Yao Yao, Yulong Lu, Gilad Lerman
This paper investigates feature learning within the framework of the deep Ritz method for solving the stationary Schrödinger equation with Neumann boundary conditions. We first ana…
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs
Yuxuan Zhao, Yulong Lu
We study the posterior contraction rate of Bayesian Physics-Informed Neural Networks (PINNs) for solving a general class of elliptic partial differential equations (PDEs). We focus…
A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schrödinger Equations
Frank Cole, Yulong Lu, Shaurya Sehgal
We address the following question: given a collection of independent random matrices drawn from a common distribution $…
In-Context Operator Learning on the Space of Probability Measures
Frank Cole, Dixi Wang, Yineng Chen +2
We introduce \emph{in-context operator learning on probability measure spaces} for optimal transport (OT). The goal is to learn a single solution operator that maps a pair of distr…