51 citations · 66 across the 10 of their papers we have counts for
11 papers
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…
Theory-to-Practice Gap for Neural Networks and Neural Operators
Philipp Grohs, Samuel Lanthaler, Margaret Trautner
This work studies the sampling complexity of learning with ReLU neural networks and neural operators. For mappings belonging to relevant approximation spaces, we derive upper bound…
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…
An operator learning perspective on parameter-to-observable maps
Daniel Zhengyu Huang, Nicholas H. Nelsen, Margaret Trautner
Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map bet…
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 macroscopic internal variables and history dependence from microscopic models
Burigede Liu, Eric Ocegueda, Margaret Trautner +2
This paper concerns the study of history dependent phenomena in heterogeneous materials in a two-scale setting where the material is specified at a fine microscopic scale of hetero…
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…
Learn Like The Pro: Norms from Theory to Size Neural Computation
Margaret Trautner, Ziwei Li, Sai Ravela
The optimal design of neural networks is a critical problem in many applications. Here, we investigate how dynamical systems with polynomial nonlinearities can inform the design of…
Informative Neural Ensemble Kalman Learning
Margaret Trautner, Gabriel Margolis, Sai Ravela
In stochastic systems, informative approaches select key measurement or decision variables that maximize information gain to enhance the efficacy of model-related inferences. Neura…
Neural Integration of Continuous Dynamics
Margaret Trautner, Sai Ravela
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numer…