A Computational Framework for Solving Wasserstein Lagrangian Flows
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: optimal transport, Schrödinger bridge, trajectory inference, single-cell
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
TL;DR: extension of the optimal transport via considering Lagrangians on the density manifold
Abstract: The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (_kinetic energy_), and the regularization of density paths (_potential energy_). These combinations yield different variational problems (_Lagrangians_), encompassing many variations of the optimal transport problem such as the Schrödinger bridge, unbalanced optimal transport, and optimal transport with physical constraints, among others. In general, the optimal density path is unknown, and solving these variational problems can be computationally challenging. Leveraging the dual formulation of the Lagrangians, we propose a novel deep learning based framework approaching all of these problems from a unified perspective. Our method does not require simulating or backpropagating through the trajectories of the learned dynamics, and does not need access to optimal couplings. We showcase the versatility of the proposed framework by outperforming previous approaches for the single-cell trajectory inference, where incorporating prior knowledge into the dynamics is crucial for correct predictions.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
Supplementary Material: zip
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 4210
Loading