AI RESEARCH
Schr\"odinger Bridge Over A Compact Connected Lie Group
arXiv CS.LG
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ArXi:2603.14049v1 Announce Type: cross This work studies the Schr\"odinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial and terminal densities ed over the Lie group while minimizing the control effort. We develop a coordinate-free formulation of this stochastic optimal control problem that respects the underlying geometric structure of the Lie group, thereby avoiding limitations associated with local parameterizations or embeddings in Euclidean spaces.