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<p>We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability with respect to perturbations to the problem data, we show convergence of spatial discretizations. Our framework accommodates various standard low-rank tensor formats for multivariate functions, including tensor train and hierarchical tensors.</p>

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Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月23日

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  • Markus Bachmayr,
  • Henrik Eisenmann,
  • André Uschmajew

摘要

We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability with respect to perturbations to the problem data, we show convergence of spatial discretizations. Our framework accommodates various standard low-rank tensor formats for multivariate functions, including tensor train and hierarchical tensors.