Work

A deep learning approach to multi-marginal optimal transport via Hilbert space embeddings of probability measures

Year: 2026

Type: article

Abstract: We propose a numerical method for solving the multi-marginal Monge problem, which extends the classical Monge formulation to settings involving multiple target distributions. Our approach is based on the Hilbert space embedding of probability measures and employs a penalization technique using the maximum mean discrepancy to enforce marginal constraints. The method is designed to be computationally efficient, enabling GPU-based implementation suitable for large-scale problems. We confirm the effectiveness of the proposed method through numerical experiments using synthetic data.

Source: Statistics and Computing

DOI: 10.1007/s11222-026-10871-3

Authors: Yumiharu Nakano, Takafumi Saito

Institution: Institute of Science Tokyo

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funder: Japan Society for the Promotion of Science