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An Experimental and Finite Element Protocol to Investigate the Transport of Neutral and Charged Solutes across Articular Cartilage
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Optimal transport at finite temperature.

Patrice Koehl1, Marc Delarue2, Henri Orland3

  • 1Department of Computer Science and Genome Center, University of California, Davis, California 95616, USA.

Physical Review. E
|September 11, 2019
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Summary

This study introduces a statistical physics approach to solve optimal transport (OT) problems, offering a computationally efficient and theoretically sound alternative to existing methods for complex data analysis.

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Area of Science:

  • Probability and Mathematics
  • Statistical Physics
  • Machine Learning
  • Data Science

Background:

  • Optimal transport (OT) offers theoretical solutions but faces computational challenges for large datasets.
  • Entropy regularization accelerates approximate OT solutions but raises concerns about numerical convergence and physical interpretation.

Purpose of the Study:

  • To propose a novel approach for solving discrete optimal transport problems using statistical physics.
  • To develop a robust framework for temperature annealing in OT approximations.
  • To demonstrate the applicability of the proposed method in applied fields like protein fold recognition.

Main Methods:

  • Formulating a discrete optimal transport problem using techniques from statistical physics.
  • Deriving a strongly concave effective free energy function to capture OT constraints.
  • Defining a temperature-dependent OT pseudo-distance satisfying triangular inequalities.

Main Results:

  • The proposed method achieves a time complexity comparable to regularized OT algorithms.
  • The derived pseudo-distance monotonically converges to the standard OT distance.
  • The framework provides a clear physical interpretation for the regularization process.

Conclusions:

  • The statistical physics approach offers a competitive and theoretically grounded method for solving optimal transport problems.
  • This framework enhances the understanding and application of OT in diverse scientific domains.
  • The method shows promise for applications such as protein fold recognition using sequence data.