Research
Convex Physics Informed Neural Networks for the Monge-Ampere Optimal Transport Problem
arXiv:2501.10162v3 Announce Type: replace-cross Abstract: Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous m
arXiv:2501.10162v3 Announce Type: replace-cross Abstract: Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neural network method is advocated here for the solution of the corresponding generalized Monge-Ampere equation. Convex neural networks are advocated to enforce the convexity of the solution to the Monge-Ampere equation and obtain a suitable approximation of the optimal transport map. A particular focus is set on the enforcement of transport boundary conditions in the loss function. Numerical experiments illustrate the solution to the optimal transport problem in several configurations, and sensitivity analyses are performed.
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Source: arXiv cs.LG | 2026-09-30