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Mathematics

D-Index
45
Citations
7884
World Ranking
1474
National Ranking
83

Overview

Reinhold Schneider is affiliated with the Technical University of Berlin in Germany. Their research intersects multiple fields including Engineering, Mathematics, and Physics and Astronomy. The scientist's work spans several specialized subfields such as Statistical and Nonlinear Physics, Computational Mechanics, Computational Mathematics, Statistics, Probability and Uncertainty, and Artificial Intelligence.

The scientific contributions of Reinhold Schneider are documented through a consistent publication record across various academic venues. Frequent publication outlets include:

  • arXiv (Cornell University)
  • Constructive Approximation
  • SIAM Journal on Scientific Computing
  • Journal of Scientific Computing
  • Multiscale Modeling and Simulation

Reinhold Schneider's recent papers include the following titles:

  • A Theoretical Analysis of Deep Neural Networks and Parametric PDEs (2021) - Constructive Approximation
  • Approximating Optimal feedback Controllers of Finite Horizon Control Problems Using Hierarchical Tensor Formats (2022) - SIAM Journal on Scientific Computing
  • Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks (2021) - Journal of Scientific Computing
  • Approximative Policy Iteration for Exit Time Feedback Control Problems Driven by Stochastic Differential Equations using Tensor Train Format (2022) - Multiscale Modeling and Simulation
  • Convergence bounds for empirical nonlinear least-squares (2021) - ESAIM. Mathematical modelling and numerical analysis

Their frequent coauthors include Mathias Oster, Leon Sallandt, Martin Eigel, Philipp Trunschke, and Gitta Kutyniok. The scientist has collaborated most often with Mathias Oster, followed by Leon Sallandt and Martin Eigel.

Reinhold Schneider's research mainly concentrates on topics related to Model Reduction and Neural Networks, Tensor decomposition and applications, Advanced Numerical Methods in Computational Mathematics, Probabilistic and Robust Engineering Design, Sparse and Compressive Sensing Techniques, Mathematical Approximation and Integration, and Neural Networks and Applications.

This profile reflects a research trajectory marked by engagement with computational and numerical methods applied to complex problems in mathematics and engineering, notably involving neural networks, tensor formats, and probabilistic approaches.

Best Publications

  • Daubechies wavelets as a basis set for density functional pseudopotential calculations

    Luigi Genovese;Alexey Neelov;Stefan Goedecker;Thierry Deutsch

  • The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format

    Sebastian Holtz;Thorsten Rohwedder;Reinhold Schneider

  • Tensor product methods and entanglement optimization for ab initio quantum chemistry

    Szilard Szalay;Max Pfeffer;Valentin Murg;Gergely Barcza

  • On manifolds of tensors of fixed TT-rank

    Sebastian Holtz;Thorsten Rohwedder;Reinhold Schneider

  • Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution

    Wolfgang Dahmen;S. Prössdorf;Reinhold Schneider

  • On the low-rank approximation by the pivoted Cholesky decomposition

    Helmut Harbrecht;Michael Peters;Reinhold Schneider

  • Wavelets on Manifolds I: Construction and Domain Decomposition

    Wolfgang Dahmen;Reinhold Schneider

  • Multiskalen- und Wavelet-Matrixkompression: Analysisbasierte Methoden zur effizienten Lösung großer vollbesetzter Gleichungssysteme

    Reinhold Schneider

  • Composite wavelet bases for operator equations

    Wolfgang Dahmen;Reinhold Schneider

  • A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

    Gitta Kutyniok;Gitta Kutyniok;Philipp Petersen;Mones Raslan;Reinhold Schneider

  • Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors

    Christian Lubich;Thorsten Rohwedder;Reinhold Schneider;Bart Vandereycken

  • Compression Techniques for Boundary Integral Equations---Asymptotically Optimal Complexity Estimates

    Wolfgang Dahmen;Helmut Harbrecht;Reinhold Schneider

  • Low rank tensor recovery via iterative hard thresholding

    Holger Rauhut;Reinhold Schneider;Zeljka Stojanac;Zeljka Stojanac

  • An analysis for the DIIS acceleration method used in quantum chemistry calculations

    Thorsten Rohwedder;Reinhold Schneider

  • Convergence Results for Projected Line-Search Methods on Varieties of Low-Rank Matrices Via Łojasiewicz Inequality

    Reinhold Schneider;André Uschmajew

  • Wavelet approximation methods for pseudodifferential equations: I Stability and convergence

    W. Dahmen;S. Prössdorf;R. Schneider

  • Sparse second moment analysis for elliptic problems in stochastic domains

    Helmut Harbrecht;Reinhold Schneider;Christoph Schwab

  • Multiwavelets for Second-Kind Integral Equations

    Tobias von Petersdorff;Christoph Schwab;Reinhold Schneider

  • Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations

    Markus Bachmayr;Reinhold Schneider;André Uschmajew

  • Stable multiscale bases and local error estimation for elliptic problems

    Stephan Dahlke;Wolfgang Dahmen;Reinhard Hochmuth;Reinhold Schneider

Frequent Co-Authors

Helmut Harbrecht
Helmut Harbrecht University of Basel
Wolfgang Dahmen
Wolfgang Dahmen University of South Carolina
Wolfgang Hackbusch
Wolfgang Hackbusch Max Planck Institute for Mathematics in the Sciences
Boris N. Khoromskij
Boris N. Khoromskij Max Planck Institute for Mathematics in the Sciences
Frank Verstraete
Frank Verstraete Ghent University
Martin Costabel
Martin Costabel University of Rennes
Sebastian Wolf
Sebastian Wolf Heidelberg University
Holger Rauhut
Holger Rauhut RWTH Aachen University
Rupert Klein
Rupert Klein Freie Universität Berlin

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