WIAS Preprint No. 2444, (2017)

Non-intrusive tensor reconstruction for high dimensional random PDEs


  • Eigel, Martin
  • Neumann, Johannes
  • Schneider, Reinhold
  • Wolf, Sebastian

2010 Mathematics Subject Classification

  • 35R60 47B80 60H35 65C20 65N12 65N22 65J10


  • non-intrusive, tensor reconstruction, partial differential equations with random coefficients, tensor representation, tensor train, uncertainty quantification, low-rank




This paper examines a completely non-intrusive, sample-based method for the computation of functional low-rank solutions of high dimensional parametric random PDEs which have become an area of intensive research in Uncertainty Quantification (UQ). In order to obtain a generalized polynomial chaos representation of the approximate stochastic solution, a novel black-box rank-adapted tensor reconstruction procedure is proposed. The performance of the described approach is illustrated with several numerical examples and compared to Monte Carlo sampling.

Appeared in

  • Comput. Methods Appl. Math., 19 (2019), pp. 39--53 (published online on 25.07.2018), DOI 10.1515/cmam-2018-0028 .

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