TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics

By Alexander Tong, Jessie Huang, Guy Wolf, David van Dijk, Smita Krishnaswamy. 2020

287 citations recorded by the source corpus.

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model continuous dynamics and non-linear paths that entities can take in these systems. To address this issue, we establish a link between continuous normalizing flows and dynamic optimal transport, that allows us to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present TrajectoryNet, which controls the continuous paths taken between distributions to produce dynamic optimal transport. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.

Subfields: Molecular Biology, Statistics and Probability, Water Science and Technology

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In Molecular Biology

1. Eric Vanden-Eijnden
2. Michael S. Albergo
3. Paul C. Bressloff

In Statistics and Probability

1. Michael S. Albergo
2. Nicholas Matthew Boffi
3. Eric Vanden-Eijnden

Citations in the corpus

• Flow Matching for Generative Modeling (2022, neutral): “…regularize the ODE to be easier to solve, e.g. , using augmentation (Dupont et al., 2019), adding regularization terms (Yang & Karniadakis, 2019; Finlay et al., 2020; Onken et al., 2021; Tong et al., 2020; Kelly et al., 2020), or stochastically sampling the integration interval (Du et al., 2022).”
• Stochastic Interpolants: A Unifying Framework for Flows and Diffusions (2023, methodology): “Optimal transport perspectives in flow-based methods have primarily been employed as a regularization penalty [51, 34, 14, 46] or via imposing structure on the parameterization itself [19, 50].”