Hopf-Cole transformation via generalized Schrodinger bridge problem

Flavien Leger UCLA Wuchen Li UCLA

Differential Geometry Dynamical Systems Information Theory Probability mathscidoc:2004.10001

arXiv:1901.09051, 2019.1
We study generalized Hopf–Cole transformations motivated by the Schrödinger bridge problem, which can be seen as a boundary value Hamiltonian system on the Wasserstein space. We prove that generalized Hopf–Cole transformations are symplectic submersions in the Wasserstein symplectic geometry. Many examples, including a Hopf–Cole transformation for the shallow water equations, are given. Based on this transformation, energy splitting inequalities are provided.
Optimal transport; Information geometry; Geometric analysis; Machine learning
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@inproceedings{flavien2019hopf-cole,
  title={Hopf-Cole transformation via generalized Schrodinger bridge problem},
  author={Flavien Leger, and Wuchen Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200427015606163260652},
  booktitle={arXiv:1901.09051},
  year={2019},
}
Flavien Leger, and Wuchen Li. Hopf-Cole transformation via generalized Schrodinger bridge problem. 2019. In arXiv:1901.09051. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200427015606163260652.
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