Transport Problem

The transport problem encompasses the mathematical challenge of efficiently moving entities (mass, information, or objects) between different locations, often optimizing for cost or time. Current research focuses on developing robust and efficient algorithms, such as those based on optimal transport (including Sinkhorn iterations and β-potential regularization) and neural networks, to solve both forward and inverse transport problems across diverse applications. These advancements are improving the accuracy and speed of solutions in areas ranging from environmental modeling (e.g., contaminant source identification) to machine learning (e.g., few-shot learning and time series forecasting), highlighting the broad significance of this field. A key emerging theme is the importance of considering inherent data properties, like stationarity, when developing and evaluating transport models.