51 citations · 66 across the 10 of their papers we have counts for
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Enforcing Dirichlet Boundary Conditions in Operator Learning
Andrew M. Stuart, Margaret Trautner
Operator learning in scientific machine learning is concerned with approximation of maps between infinite-dimensional function spaces; such maps frequently arise as the solution op…
Learning Memory and Material Dependent Constitutive Laws
Kaushik Bhattacharya, Lianghao Cao, George Stepaniants +2
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale…
Discretization Error of Fourier Neural Operators
Samuel Lanthaler, Andrew M. Stuart, Margaret Trautner
Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main mode…
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…
Learning Markovian Homogenized Models in Viscoelasticity
Kaushik Bhattacharya, Burigede Liu, Andrew M. Stuart +1
Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homog…