We propose a principled physics-based approach to impose constraints flexibly in such optimal transport problems. Constraints are included in mirror descent dynamics using the principle of D'Alembert-Lagrange from classical mechanics. This leads to a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates.
Traffic congestion is one of the major challenges faced by the transportation industry. While this problem carries a high economic and environmental cost, the need for an efficient design of optimal paths for passengers in multilayer network infrastructures is imperative. We consider an approach based on optimal transport theory to route passengers preferably along layers that are more carbon-efficient than the road, e.g., rails.
Modeling traffic distribution and extracting optimal flows in multilayer networks is of the utmost importance to design efficient, multi-modal network infrastructures. Here, we adapt these results to study how optimal flows distribute on multilayer networks. We propose a model where optimal flows on different layers contribute differently to the total cost to be minimized.
Detecting communities in networks is important in various domains of applications. We present an OT-based approach that exploits recent advances in OT theory to allow tuning for traffic penalization, which enforces different transportation schemes.
Analysis of Titanic shipwreck is essential in order to understand the historical data. The correlation between the independent and dependent features was observed in order to determine features that may have impact on passenger survival. In this paper, we explored the Titanic data and four machine learning algorithms.
Machine learning and data-driven techniques have become very famous and significant in several areas in recent times. In this paper, we discuss the performances of some machine learning methods on both loan approval.