What question did this study set out to answer?

The central aim is to develop a discrete formulation of the Schrödinger bridge problem for efficient interpolation between probability distributions.

Schrödinger Bridges on Discretized Geometric Domains

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Randomized trial demonstrates improved interpolation accuracy in geometric domains, suggesting enhanced computational efficiency.

The central aim is to develop a discrete formulation of the Schrödinger bridge problem for efficient interpolation between probability distributions.
Introduced a dual formulation using entropy-regularized optimal transport and the log-heat equation.
Implemented a Sinkhorn algorithm with heat kernel application and multiplicative updates.
Demonstrated application across various mesh- and grid-based problems.
Produced sharper interpolants compared to Wasserstein barycenters with a specific level of regularization.
Achieved exact endpoint marginals and faster computations.
Showed scalability to high-resolution meshes and finer temporal discretizations.

Silva et al. (2026) studied this question.

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