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SYNCHRONIZED OPTIMAL TRANSPORT FOR JOINT MODELING OF DYNAMICS ACROSS MULTIPLE SPACES.

Zixuan Cang1, Yanxiang Zhao2

  • 1Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695 USA.

SIAM Journal on Applied Mathematics
|September 2, 2025
PubMed
Summary
This summary is machine-generated.

Synchronized optimal transport (SyncOT) jointly models system dynamics across multiple spaces. This novel approach ensures coherence in complex, multifaceted data analysis for improved scientific insights.

Keywords:
35Q4949Q22Yan algorithmdynamical optimal transportmultiple spacesprimal-dual methods

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Area of Science:

  • * Computational mathematics
  • * Data science
  • * Dynamical systems

Background:

  • * Optimal transport is vital for reconstructing dynamics from complex data.
  • * Multifaceted data requires maintaining dynamic coherence across diverse spaces.
  • * Existing methods struggle with joint modeling of dynamics across multiple representations of a system.

Purpose of the Study:

  • * To introduce Synchronized Optimal Transport (SyncOT) for jointly modeling dynamics across multiple spaces.
  • * To ensure coherence of system dynamics represented in diverse data spaces.
  • * To develop efficient algorithms for solving the SyncOT problem.

Main Methods:

  • * Formulation of SyncOT as a convex optimization problem.
  • * Discretization of the problem using a staggered grid.
  • * Development of primal-dual algorithms for efficient computation.

Main Results:

  • * SyncOT effectively models synchronized dynamics across multiple spaces.
  • * Numerical experiments demonstrate SyncOT's capabilities and properties.
  • * The proposed algorithms are validated for their effectiveness.

Conclusions:

  • * SyncOT provides a robust framework for analyzing systems with multifaceted data.
  • * The method ensures consistency of dynamics across different data representations.
  • * SyncOT advances the application of optimal transport in complex data analysis.