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κ-statistics approach to optimal transport waveform inversion.

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This study introduces a new method combining optimal transport theory and κ-statistical thermodynamics to solve phase ambiguity in waveform analysis. The approach enhances physical parameter extraction in complex scientific and geophysical problems.

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Area of Science:

  • Physics
  • Geophysics
  • Statistical Thermodynamics

Background:

  • Extracting unmeasurable physical parameters from data is challenging.
  • Phase ambiguity in waveforms hinders physical model construction.

Purpose of the Study:

  • To present a novel approach for mitigating phase ambiguity in waveform-driven problems.
  • To improve the accuracy of physical parameter extraction.

Main Methods:

  • Combining optimal transport theory with κ-statistical thermodynamics.
  • Constructing an energy function using a κ-Gaussian distribution to create an optimal transport metric.

Main Results:

  • The proposed method outperforms classical frameworks in geophysical inverse problems.
  • Demonstrated effectiveness on a nonlinear, wave-equation-based numerical solution.

Conclusions:

  • The κ-generalized optimal transport metric offers a versatile solution for various inverse problems.
  • Applicable to power-law exponent estimation and quantum mechanics machine learning.