This paper proposes a novel deep learning-based framework for solving variational problems, with a focus on optimal transport. The dynamical formulation of optimal transport can be extended through different choices of underlying geometry and regularization of density paths. These combinations yield different variational problems, which are computationally challenging to solve. The authors use the dual formulation of Lagrangians to approach these problems from a unified perspective. The proposed method does not require simulating or backpropagating through the trajectories of the learned dynamics, and does not need access to optimal couplings. The versatility of the proposed framework is demonstrated by its superior performance in single-cell trajectory inference, where incorporating prior knowledge into the dynamics is crucial for making accurate predictions.
Publication date: 16 Oct 2023
Project Page: https://arxiv.org/abs/2310.10649v1
Paper: https://arxiv.org/pdf/2310.10649
