MST-Direct scales exact multivariate geostatistical simulation via Sinkhorn transport

Tcharlies Bachmann Schmitz has published MST‑Direct at Scale, extending the original Matching‑via‑Sinkhorn‑Transport approach from small bivariate to large multivariate and conditional geostatistical simulations. The new method addresses three key limitations: scalability beyond a few thousand nodes through a sparse, candidate‑restricted Sinkhorn matcher with O(nC) memory complexity; multivariate support by matching target value tuples onto an independent FFT‑MA Gaussian backbone that reproduces a prescribed variogram; and hard‑data conditioning by fixing observed data tuples at their spatial locations while conditioning the backbone via kriging. Because the transport plan remains a permutation, the multivariate joint distribution is preserved exactly.

Validation on the same six‑variate, heteroscedastic, strongly nonlinear reference distribution used in Direct Multivariate Simulation (DMS) shows zero histogram error, exact hard data honoring, and accurate spatial correlation reproduction under both unconditional (200×200) and conditional (100×100 grid with 200 hard data) scenarios. Benchmarking against Projection Pursuit Multivariate Transform (PPMT) confirms MST‑Direct’s exactness, while PPMT remains an approximation. This breakthrough enables practitioners in mining, oil & gas, and environmental modeling to run large‑scale multivariate simulations without distributional distortions.