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About this paper
Yesom Park, Shu Liu, Mo Zhou, Stanley Osher
Neural characteristic flow (NCF) learns bidirectional optimal-transport maps from one Hamilton–Jacobi solution, whose characteristics yield straight paths and explicit endpoints without numerical ODE integration. Its implicit-solution and distribution-matching losses train the model. On a dimension-64 Gaussian benchmark, NCF’s UVP is 0.858%, below HJ-PINN’s 1.683% but above MM-v1’s 0.415%; experiments use quadratic cost.
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