anyakrakusuma: A Python Library for Entropic Schrödinger Bridges on Idealized Geometries
2026-07-20 • Mathematical Software
Mathematical Software
AI summaryⓘ
The authors introduce anyakrakusuma, a free Python tool that solves a math problem linking two sets of points using an approach called the discrete static Schrödinger bridge, related to optimal transport. Their method uses a stable computation technique (log-domain Sinkhorn–Knopp iteration) to handle challenging numerical situations and accurately find smooth transformations between point clouds. They test the tool on several made-up curved shapes and show it can precisely capture changes like rotations and deformations with detailed diagnostic measures. However, the examples are synthetic, and applying the tool to real data will need further exploration.
Schrödinger bridgeoptimal transportSinkhorn–Knopp iterationentropic interpolationlog-domain computationcovariance analysisdifferential entropypoint cloudsGibbs kernelmarginal fidelity
Authors
Sandy Hardian Susanto Herho, Dasapta Erwin Irawan, Agus Wahyu Jatmiko, Sito Fossy Biosa, Candrasa Surya Dharma, Edi Riawan, Astyka Pamumpuni, Rendy Dwi Kartiko, Rusmawan Suwarman, Deny Juanda Puradimaja
Abstract
We present anyakrakusuma, an open-source Python library that solves the discrete static Schrödinger bridge problem, the entropically regularized counterpart of optimal transport, through a log-domain Sinkhorn--Knopp iteration and reconstructs the entropic interpolation between two empirical point clouds. The solver is paired with a diagnostic pipeline that characterizes the optimal coupling and the intermediate distributions through information-theoretic and geometric measures. We exercise the library on four idealized planar cases spanning a circle-to-circle dilation, a spiral-to-mixture fragmentation, a rigid reorientation of two moons, and a Lissajous-to-trefoil deformation. The log-domain formulation is necessary rather than merely convenient at the parameters studied, where the cost-to-regularization ratio reaches four hundred and the Gibbs kernel underflows double precision across most of its range; the iteration nonetheless attains a marginal residual of $10^{-9}$ and unit marginal fidelity in every case. Residual histories decay geometrically over approximately eight decades at per-iteration contraction factors between $0.966$ and $0.976$, which are local rates near the fixed point that lie many orders of magnitude below the worst-case Hilbert-metric bound. The covariance analysis recovers an imposed ninety-degree reorientation to within $0.07^\circ$, roughly forty times smaller than its uncertainty, across a masked interval of near-isotropy on which the principal axis is unobservable. The diagnostics are reported with explicit attention to the regimes in which each is well defined, including the differential entropy, which is meaningful only on the open interpolation interval. The presented cases are constructed rather than measured; quantitative application to empirical point clouds requires further study.