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      Numerical Approximation of High-Dimensional Gibbs Distributions Using the Functional Hierarchical Tensor

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          Abstract

          The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant calculations. This work addresses this challenge by performing a particle-based high-dimensional parametric density estimation subroutine, and the input to the subroutine is Gibbs samples generated by leveraging advanced sampling techniques. Specifically, to generate Gibbs samples, we employ ensemble-based annealed importance sampling, a population-based approach for sampling multimodal distributions. These samples are then processed using functional hierarchical tensor sketching, a tensor-network-based density estimation method for high-dimensional distributions, to obtain the numerical representation of the Gibbs distribution. We successfully apply the proposed approach to complex Ginzburg-Landau models with hundreds of variables. In particular, we show that the approach proposed is successful at addressing the metastability issue under difficult numerical cases.

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          Author and article information

          Journal
          28 January 2025
          Article
          2501.17143
          54df3e1e-a83a-4090-a43e-057dac08e720

          http://creativecommons.org/licenses/by/4.0/

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          Custom metadata
          math.NA cs.NA physics.comp-ph physics.data-an

          Numerical & Computational mathematics,Mathematical & Computational physics

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