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Recursive Linear Tensor Expansion with Natural Occupation Analysis.

Zeynep Gündoğar1, Mads Greisen Ho̷jlund2, Kasper Green Larsen1

  • 1Department of Computer Science, University of Aarhus, DK-8000 Aarhus C, Denmark.

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This summary is machine-generated.

This study presents a novel recursive tensor decomposition method inspired by quantum chemistry. The algorithm accurately reconstructs tensors using smaller components and matrix transformations, applicable to diverse datasets.

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Area of Science:

  • Quantum Chemistry
  • Computational Science
  • Data Analysis

Background:

  • Tensor decomposition is crucial for analyzing complex datasets.
  • Existing methods may lack efficiency or accuracy for certain applications.
  • Quantum chemical theories offer advanced concepts for data representation.

Purpose of the Study:

  • To introduce a new recursive tensor decomposition method.
  • To integrate quantum chemical principles like natural occupation numbers and basis sets.
  • To develop a numerical technique for precise tensor reconstruction.

Main Methods:

  • Recursive algorithms combining linear expansion and natural basis transformations.
  • Truncation strategies inspired by configuration interaction theory.
  • A Python implementation for 3D tensor decomposition into vectors and matrices.

Main Results:

  • The Recursive Linear Tensor Expansion in Natural basis (RLTE-NB) algorithm ensures convergence.
  • Precise tensor reconstruction achieved using subtensors and matrix transformations.
  • Successful application to random, experimental, and quantum chemical datasets (e.g., water vibrational wave functions).

Conclusions:

  • The RLTE-NB algorithm offers a robust and accurate tensor decomposition technique.
  • Demonstrated applicability and accuracy control in quantum chemistry calculations (e.g., density fitting, correlation energy).
  • Potential for broad applications in scientific data analysis and computational modeling.