Transport Map

Transport maps are mathematical tools used to transform probability distributions, aiming to efficiently move samples from a simple source distribution to a complex target distribution. Current research focuses on developing and improving these maps using various architectures, including normalizing flows (often implemented as neural ordinary differential equations), and algorithms that leverage techniques like annealing, stochastic sampling, and optimal transport. This work is significant because efficient and accurate transport maps are crucial for diverse applications such as generative modeling, Bayesian inference, and domain adaptation, enabling improved sampling from high-dimensional and multi-modal distributions and facilitating solutions to challenging optimization problems.