Deep Neural Networks Are Effective At Learning High-Dimensional
Hilbert-Valued Functions From Limited Data

Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data

11 December 2020

Simone Brugiapaglia

Papers citing "Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data"

18 / 18 papers shown

Title
Operator Learning Using Random Features: A Tool for Scientific Computing Nicholas H. Nelsen Andrew M. Stuart 37 12 0 12 Aug 2024
Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics Simone Brugiapaglia N. Dexter Samir Karam Weiqi Wang AI4CE DiffM 37 1 0 03 Jun 2024
Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 37 4 0 04 Apr 2024
Response Theory via Generative Score Modeling L. T. Giorgini Katherine Deck Tobias Bischoff Andre N. Souza 38 9 0 01 Feb 2024
A practical existence theorem for reduced order models based on convolutional autoencoders N. R. Franco Simone Brugiapaglia AI4CE 29 4 0 01 Feb 2024
A unified framework for learning with nonlinear model classes from arbitrary linear samples Ben Adcock Juan M. Cardenas N. Dexter 29 3 0 25 Nov 2023
Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometries Haitz Sáez de Ocáriz Borde Anastasis Kratsios 31 4 0 23 Oct 2023
Active Learning for Single Neuron Models with Lipschitz Non-Linearities Aarshvi Gajjar C. Hegde Christopher Musco 14 11 0 24 Oct 2022
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning Ben Adcock Juan M. Cardenas N. Dexter 25 8 0 25 Aug 2022
Compressive Fourier collocation methods for high-dimensional diffusion equations with periodic boundary conditions Weiqi Wang Simone Brugiapaglia 17 2 0 02 Jun 2022
Optimal Learning P. Binev A. Bonito Ronald A. DeVore G. Petrova FedML 30 0 0 30 Mar 2022
On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 9 9 0 25 Mar 2022
A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks Xiaoyu Ma S. Sardy N. Hengartner Nikolai Bobenko Yen Ting Lin 19 2 0 21 Jan 2022
Convergence Rates for Learning Linear Operators from Noisy Data Maarten V. de Hoop Nikola B. Kovachki Nicholas H. Nelsen Andrew M. Stuart 6 54 0 27 Aug 2021
$Neural Network Training Using $\ell_1$-Regularization and Bi-fidelity Data$ Neural Network Training Using $\ell_1$ -Regularization and Bi-fidelity Data Subhayan De Alireza Doostan 13 24 0 27 May 2021
The Random Feature Model for Input-Output Maps between Banach Spaces Nicholas H. Nelsen Andrew M. Stuart 13 140 0 20 May 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Moritz Geist P. Petersen Mones Raslan R. Schneider Gitta Kutyniok 16 83 0 25 Apr 2020
The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems N. Gottschling Vegard Antun A. Hansen Ben Adcock 24 31 0 05 Jan 2020