447 citations · 3.6k across the 105 of their papers we have counts for
119 papers
Bayesian statistical inverse problems for a coupled Fokker-Planck-Darcy system
Grigorios A. Pavliotis, Andrew M. Stuart, Andrea Zanoni
We study the nonparametric statistical inverse problem of recovering the space-dependent permittivity in a coupled Fokker-Planck-Darcy system from discrete, noisy observations of t…
Filtering Dynamical Systems Using Observations of Statistics
Eviatar Bach, Tim Colonius, Isabel Scherl +1
We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $…
The Parametric Complexity of Operator Learning
Samuel Lanthaler, Andrew M. Stuart
Neural operator architectures employ neural networks to approximate operators mapping between Banach spaces of functions; they may be used to accelerate model evaluations via emula…
Learning Homogenization for Elliptic Operators
Kaushik Bhattacharya, Nikola Kovachki, Aakila Rajan +2
Multiscale partial differential equations (PDEs) arise in various applications, and several schemes have been developed to solve them efficiently. Homogenization theory is a powerf…
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs
Pau Batlle, Yifan Chen, Bamdad Hosseini +2
We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assump…
Nonlocality and Nonlinearity Implies Universality in Operator Learning
Samuel Lanthaler, Zongyi Li, Andrew M. Stuart
Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engin…