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09/03/2023
Distribution learning via neural differential equations: a nonparametric statistical perspective
Ordinary differential equations (ODEs), via their induced flow maps, pro...
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07/19/2023
Deep Operator Network Approximation Rates for Lipschitz Operators
We establish universality and expression rate bounds for a class of neur...
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12/14/2022
Multilevel Domain Uncertainty Quantification in Computational Electromagnetics
We continue our study [Domain Uncertainty Quantification in Computationa...
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07/11/2022
Neural and gpc operator surrogates: construction and expression rate bounds
Approximation rates are analyzed for deep surrogates of maps between inf...
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04/28/2022
Multilevel Optimization for Inverse Problems
Inverse problems occur in a variety of parameter identification tasks in...
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01/14/2022
De Rham compatible Deep Neural Networks
We construct several classes of neural networks with ReLU and BiSU (Bina...
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01/06/2022
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
We establish summability results for coefficient sequences of Wiener-Her...
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11/13/2021
Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in L^2(ℝ^d,γ_d)
For artificial deep neural networks, we prove expression rates for analy...
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07/28/2021
Sparse approximation of triangular transports. Part II: the infinite dimensional case
For two probability measures ρ and π on [-1,1]^ℕ we investigate the appr...
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06/12/2020