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Optimal transport — the geometry of moving probability
fluid probability dynamics
Benamou–Brenier: the distance between two distributions is the least kinetic energy of a fluid that carries one to the other, subject to the continuity equation. Jordan–Kinderlehrer–Otto (1998): the Fokker–Planck equation is the gradient flow of free energy F = ∫ρ log ρ + ∫Uρ in this Wasserstein geometry — diffusion is steepest descent of entropy.
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adjoining cards
- instantiates → Fluid probability dynamics — one continuity equation across physics, geometry, and ML
- on the shelf of → The created order — the science of the floor — a member of the science shelf in the keeping
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