相关论文: Learning stochastic dynamics from snapshots throug…

Recovering the dynamics from a few snapshots of a high-dimensional system is a challenging task in statistical physics and machine learning, with important applications in computational biology. Many algorithms have been developed to tackle…

Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis. Existing unbalanced Optimal Transport (OT) methods…

The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport…

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schr\"odinger bridge theory, or their variants to…

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…

The Optimal Transport (OT) problem investigates a transport map that connects two distributions while minimizing a given cost function. Finding such a transport map has diverse applications in machine learning, such as generative modeling…

Scientists often want to make predictions beyond the observed time horizon of "snapshot" data following latent stochastic dynamics. For example, in time course single-cell mRNA profiling, scientists have access to cellular transcriptional…

Leveraging connections between diffusion-based sampling, optimal transport, and stochastic optimal control through their shared links to the Schr\"odinger bridge problem, we propose novel objective functions that can be used to transport…

The dynamic Schr\"odinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient…

Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally…

Single-cell RNA-sequencing captures a temporal slice, or a snapshot, of a cell differentiation process. A major bioinformatical challenge is the inference of differentiation trajectories from a single snapshot, and methods that account for…

Scientific data, from cellular snapshots in biology to celestial distributions in cosmology, often consists of static patterns from underlying dynamical systems. These snapshots, while lacking temporal ordering, implicitly encode the…

Mass transport problems arise in many areas of machine learning whereby one wants to compute a map transporting one distribution to another. Generative modeling techniques like Generative Adversarial Networks (GANs) and Denoising Diffusion…

In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…

In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…

We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…

In many real-world settings--e.g., single-cell RNA sequencing, mobility sensing, and environmental monitoring--data are observed only as temporally aggregated snapshots collected over finite time windows, often with noisy or uncertain…

We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…

Medical image reconstruction from measurement data is a vital but challenging inverse problem. Deep learning approaches have achieved promising results, but often requires paired measurement and high-quality images, which is typically…

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…