arXiv Machine Learning
Aug 28

COFM: Consistent Optimal Transport Flow Matching via Partially Input Convex Neural Networks

The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.

By Fanghui Song, Zhongjian Wang, Jiebao Sun
arXiv Machine Learning
Aug 27

Physics-Informed Error Field Learning: A Post-Training Optimization Framework for Physics-Informed Neural Networks

Physics-Informed Error Field Learning (PIEFL) is a post‑training optimization framework for Physics‑Informed Neural Networks (PINNs). After a primary network reaches satisfactory accuracy, PIEFL introduces an auxiliary error network that learns the discrepancy between the current approximation and the exact solution by deriving error control equations under physical constraints. The learned error correction is then combined with the primary prediction, improving solution accuracy without modifying the primary network architecture and focusing computational resources on correcting existing prediction errors.

By Jiuyun Sun, Yong Zhang
arXiv Machine Learning
Sep 17

Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization

The paper introduces a geometric framework for reinforcement learning that treats policies as mappings into the Wasserstein space of action probabilities. It establishes a Riemannian structure induced by stationary distributions, defines the tangent space of policies, and characterizes geodesics while addressing measurability concerns. The authors formulate a general RL optimization problem, construct a gradient flow via Otto's calculus, compute the gradient and Hessian of the energy, and demonstrate the approach with numerical examples for low‑dimensional problems and neural‑network‑parameterized policies for high‑dimensional settings.

By Mathias Dus (IRMA)
arXiv AI
Jun 16

Optimal Transport for Machine Learners

arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.

By Gabriel Peyr\'e
arXiv Machine Learning
Sep 11

Supply Chain Analytics: A Data-Driven Approach

The article "Supply Chain Analytics: A Data-Driven Approach" presents a mathematically rigorous framework that integrates statistical learning with robust decision-making for logistics and operations management. It covers topics from empirical demand forecasting to optimal inventory and network control under uncertainty, including sample minimization, dynamic programming for inventory replenishment, network fulfillment, and distributionally robust optimization using transport theory. The work also links predictive models with prescriptive algorithms such as column generation for vehicle routing and non‑homogeneous queueing regimes, offering both theoretical foundations and algorithmic guidance for building resilient, automated supply chain systems.

By Elioth Sanabria