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Distribution learning via neural differential equations: a nonparametric statistical perspective
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions.
Deep Operator Network Approximation Rates for Lipschitz Operators
We establish universality and expression rate bounds for a class of neural Deep Operator Networks (DON) emulating Lipschitz (or H\"older) continuous maps $\mathcal G:\mathcal X\to\mathcal Y$ between (subsets of) separable Hilbert spaces $\mathcal X$, $\mathcal Y$.
Neural and spectral operator surrogates: unified construction and expression rate bounds
Specifically, we study approximation rates for Deep Neural Operator and Generalized Polynomial Chaos (gpc) Operator surrogates for nonlinear, holomorphic maps between infinite-dimensional, separable Hilbert spaces.
De Rham compatible Deep Neural Network FEM
Our construction and DNN architecture generalizes previous results in that no geometric restrictions on the regular simplicial partitions $\mathcal{T}$ of $\Omega$ are required for DNN emulation.
Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d,γ_d)$
For artificial deep neural networks, we prove expression rates for analytic functions $f:\mathbb{R}^d\to\mathbb{R}$ in the norm of $L^2(\mathbb{R}^d,\gamma_d)$ where $d\in {\mathbb{N}}\cup\{ \infty \}$.
