Operator learning: Algorithms and analysis
Operator learning refers to the application of ideas from machine learning to approximate
(typically nonlinear) operators mapping between Banach spaces of functions. Such …
(typically nonlinear) operators mapping between Banach spaces of functions. Such …
Operator learning using random features: A tool for scientific computing
Supervised operator learning centers on the use of training data, in the form of input-output
pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful …
pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful …
A mathematical guide to operator learning
N Boullé, A Townsend - arXiv preprint arXiv:2312.14688, 2023 - arxiv.org
Operator learning aims to discover properties of an underlying dynamical system or partial
differential equation (PDE) from data. Here, we present a step-by-step guide to operator …
differential equation (PDE) from data. Here, we present a step-by-step guide to operator …
Error bounds for learning with vector-valued random features
S Lanthaler, NH Nelsen - Advances in Neural Information …, 2024 - proceedings.neurips.cc
This paper provides a comprehensive error analysis of learning with vector-valued random
features (RF). The theory is developed for RF ridge regression in a fully general infinite …
features (RF). The theory is developed for RF ridge regression in a fully general infinite …
Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem
We consider the problem of learning a linear operator $\theta $ between two Hilbert spaces
from empirical observations, which we interpret as least squares regression in infinite …
from empirical observations, which we interpret as least squares regression in infinite …
An operator learning perspective on parameter-to-observable maps
Computationally efficient surrogates for parametrized physical models play a crucial role in
science and engineering. Operator learning provides data-driven surrogates that map …
science and engineering. Operator learning provides data-driven surrogates that map …
Optimal estimation of structured covariance operators
O Al-Ghattas, J Chen, D Sanz-Alonso… - arXiv preprint arXiv …, 2024 - arxiv.org
This paper establishes optimal convergence rates for estimation of structured covariance
operators of Gaussian processes. We study banded operators with kernels that decay …
operators of Gaussian processes. We study banded operators with kernels that decay …
Covariance operator estimation: sparsity, lengthscale, and ensemble Kalman filters
O Al-Ghattas, J Chen, D Sanz-Alonso… - arXiv preprint arXiv …, 2023 - arxiv.org
This paper investigates covariance operator estimation via thresholding. For Gaussian
random fields with approximately sparse covariance operators, we establish non-asymptotic …
random fields with approximately sparse covariance operators, we establish non-asymptotic …
Domain Generalization by Functional Regression
M Holzleitner, SV Pereverzyev… - … Functional Analysis and …, 2024 - Taylor & Francis
The problem of domain generalization is to learn, given data from different source
distributions, a model that can be expected to generalize well on new target distributions …
distributions, a model that can be expected to generalize well on new target distributions …
Benign overfitting in Fixed Dimension via Physics-Informed Learning with Smooth Inductive Bias
Recent advances in machine learning have inspired a surge of research into reconstructing
specific quantities of interest from measurements that comply with certain physical laws …
specific quantities of interest from measurements that comply with certain physical laws …