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Mini-workshop: Nonlinear approximation of high-dimensional functions in scientific computing. Abstracts from the mini-workshop held October 15--20, 2023 - MaRDI portal

Mini-workshop: Nonlinear approximation of high-dimensional functions in scientific computing. Abstracts from the mini-workshop held October 15--20, 2023 (Q6613392)

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Please use this page instead for the normal view: Mini-workshop: Nonlinear approximation of high-dimensional functions in scientific computing. Abstracts from the mini-workshop held October 15--20, 2023

scientific article; zbMATH DE number 7921223

Language	Label	Description	Also known as
English	Mini-workshop: Nonlinear approximation of high-dimensional functions in scientific computing. Abstracts from the mini-workshop held October 15--20, 2023	scientific article; zbMATH DE number 7921223

Statements

scholarly article

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Mini-workshop: Nonlinear approximation of high-dimensional functions in scientific computing. Abstracts from the mini-workshop held October 15--20, 2023 (English)

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Oberwolfach Reports

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publication date

2 October 2024

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MaRDI profile type

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Tensor-Train Decomposition

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Hierarchical Singular Value Decomposition of Tensors

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Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions

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Constructive representation of functions in low-rank tensor formats

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Error bounds for approximations with deep ReLU networks

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Deep composition of tensor-trains using squared inverse Rosenblatt transports

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Scalable conditional deep inverse Rosenblatt transports using tensor trains and gradient-based dimension reduction

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Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format

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Computing Lyapunov functions using deep neural networks

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Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations

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Data-Driven Tensor Train Gradient Cross Approximation for Hamilton–Jacobi–Bellman Equations

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HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems

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TT-cross approximation for multidimensional arrays

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A proposal on machine learning via dynamical systems

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Stable architectures for deep neural networks

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A measure theoretical approach to the mean-field maximum principle for training NeurODEs

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Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors

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On the Approximability of Koopman-Based Operator Lyapunov Equations

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Error estimates for DeepONets: a deep learning framework in infinite dimensions

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The asymptotic error of chaos expansion approximations for stochastic differential equations

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Optimal approximation of piecewise smooth functions using deep ReLU neural networks

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Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\)

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Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

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Gradient descent for deep matrix factorization: dynamics and implicit bias towards low rank

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A mathematical introduction to compressive sensing

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Deep learning: a statistical viewpoint

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Approximation and estimation bounds for artificial neural networks

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On deep learning as a remedy for the curse of dimensionality in nonparametric regression

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Convergence rates for shallow neural networks learned by gradient descent

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Computer Age Statistical Inference, Student Edition

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A distribution-free theory of nonparametric regression

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On the rate of convergence of fully connected deep neural network regression estimates

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Nonparametric regression using deep neural networks with ReLU activation function

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Optimal global rates of convergence for nonparametric regression

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A sharp upper bound for sampling numbers in \(L_2\)

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Boosted optimal weighted least-squares

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Learning with tree tensor networks: complexity estimates and model selection

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Low-rank tensor methods for partial differential equations

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Adaptive low-rank methods: problems on Sobolev spaces

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Existence of dynamical low-rank approximations to parabolic problems

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Space-time adaptive wavelet methods for parabolic evolution problems

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Tree Adaptive Approximation in the Hierarchical Tensor Format

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Hierarchical Tensor Approximation of Output Quantities of Parameter-Dependent PDEs

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Adaptive stochastic Galerkin FEM

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Variational Monte Carlo -- bridging concepts of machine learning and high-dimensional partial differential equations

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.4171/OWR/2023/48

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Sitelinks

Mathematics(1 entry)

mardi Publication:6613392

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