447 citations · 3.6k across the 105 of their papers we have counts for
7 papers · 1 filter
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…
Introduction To Gaussian Process Regression In Bayesian Inverse Problems, With New ResultsOn Experimental Design For Weighted Error Measures
Tapio Helin, Andrew Stuart, Aretha Teckentrup +1
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often com…