software

Optimal transport is a thread that runs through much of our research, but the Julia ecosystem had a gap. Packages such as OptimalTransport.jl solve the discrete, entropic problem well — Sinkhorn iterations and exact linear programs over weighted point clouds. What was missing was neural optimal transport: the continuous methods that scale to high dimensions by parameterising the potential or the transport map as a neural network, and that generalise beyond the training samples. NeuralOT.jl fills that gap.

The package implements three established families of methods behind a single interface:

• solve_dualEntropic OT in high dimensions directly from samples, when you need the cost or the dual potentials.
  Seguy et al., ICLR 2018
• solve_w2Wasserstein-2 Monge maps via input-convex neural networks, when you need a valid transport map with provable convexity structure.
  Makkuva et al., ICML 2020
• flow_matchTransport-based generative models that move noise to data, with simulation-free training that scales to large datasets.
  Lipman et al., ICLR 2023

The common interface means switching methods is a one-line change. Learn a squared-cost Monge map between two distributions, then push samples through it:

result = solve_w2(sample_μ, sample_ν; dim=2, steps=2_000)
T_X    = monge_map(result, X)   # transported samples

Worked examples, installation instructions, and the method-selection guide are in the repository. The package is MIT licensed and open to contributions.