Profile of Mazen Ali

Fields of Activity / Competences

• Quantum computing
• Tensor networks and approximation
• High-dimensional partial differential equations
• Model Order Reduction and Adaptivity

Publications

Major Publications

• Ali, M.; Nouy, A.:
  Approximation of Smoothness Classes by Deep ReLU Networks.
  SINUM 2021, https://doi.org/10.1137/20M1360657.
• Ali, M.:
  Tensor Approximation and Adaptivity within Model Order Reduction.
  Dissertation 2020, http://dx.doi.org/10.18725/OPARU-25951.
• Ali, M; Steih, K; Urban, K.:
  Reduced Basis Methods with Adaptive Snapshot Computations.
  ACOM 2016, https://doi.org/10.1007/s10444-016-9485-9.

Other Publications

• Ali, M.:
  On the Ordering of Sites in the Density Matrix Renormalization Group using Quantum Mutual Information.
  2021.
• Ali, M.; Nouy, A.:
  Approximation with Tensor Networks. Part III: Multivariate Approximation.
  2021.
• Ali, M.:
  Ranks of Tensor Networks for Eigenspace Projections and the Curse of Dimensionality.
  2020.
• Ali, M.; Funken, S.A.; Schmidt, A.:
  H1-Stability of the L2-Projections onto Finite Element Spaces on Adaptively Refined Quadrilateral Meshes.
  2020.
• Ali, M.; Nouy, A.:
  Approximation with Tensor Networks. Part II: Approximation Rates for Smoothness Classes.
  2020.
• Ali, M.; Nouy, A.:
  Approximation with Tensor Networks. Part I: Approximation Spaces.
  2020.
• Ali, M.:
  Low-Rank Approximability and Entropy Area Laws for PDEs.
  2019.
• Ali, M.:
  Low-Rank Approximability and Entropy Area Laws for Ground States of Unbounded Hamiltonians.
  2019.
• Ali, M.; Nouy, A.:
  Singular Value Decomposition in Sobolev Spaces: Part II.
  2018.
• Ali, M.; Nouy, A.:
  Singular Value Decomposition in Sobolev Spaces: Part I.
  2018.
• Ali, M.; Nouy, A.:
  SVD on Intersection Spaces.
  2018.
• Ali, M.; Urban, K.:
  HT-AWGM: A Hierarchical Tucker-Adaptive Wavelet Galerkin Method for High Dimensional Elliptic Problems.
  2016.
• Ali, M.; Urban, K.:
  Reduced Basis Exact Error Estimates with Wavelets.
  2016.