Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

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 …

One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in
many realistic molecular systems, biologically important rare transitions occur on timescales …

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 …

Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and multi …

Computationally efficient surrogates for parametrized physical models play a crucial role in
science and engineering. Operator learning provides data-driven surrogates that map …

We present the first optimal rates for infinite-dimensional vector-valued ridge regression on a
continuous scale of norms that interpolate between $ L_2 $ and the hypothesis space, which …

This paper establishes optimal convergence rates for estimation of structured covariance
operators of Gaussian processes. We study banded operators with kernels that decay …

We study theoretical properties of a broad class of regularized algorithms with vector-valued
output. These spectral algorithms include kernel ridge regression, kernel principal …