AI RESEARCH
Control, Optimal Transport and Neural Differential Equations in Supervised Learning
arXiv CS.LG
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ArXi:2503.15105v4 Announce Type: replace-cross We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). specifically, we develop a novel framework for approximating unbalanced optimal transport (UOT) in the continuum using Neural ODEs. By generalizing a discrete UOT problem with Pearson divergence, we constructively design vector fields for Neural ODEs that converge to the true UOT dynamics, thereby advancing the mathematical foundations of computational transport and machine learning.