CT-OT Flow: Estimating Continuous-Time Dynamics from Discrete Temporal Snapshots

2025-05-23

AI Summary

This work addresses the challenging problem of recovering underlying continuous-time dynamics from noisy, sparse, discrete-time snapshots—without access to continuous trajectories. We propose the first framework that jointly models timestamp uncertainty and distributional evolution. Methodologically, we innovatively integrate partial optimal transport (Partial OT) for time super-resolution alignment, combined with temporal kernel smoothing and probabilistic distribution flow estimation, to construct a differentiable ODE/SDE-based dynamical model that reconstructs continuous distributional evolution paths. Evaluated on synthetic data, single-cell RNA sequencing, and typhoon trajectory datasets, our approach significantly reduces distribution reconstruction error and consistently outperforms state-of-the-art methods across all benchmarks. By enabling robust dynamics inference from highly sparse and noisy observations, our framework establishes a new paradigm for modeling dynamic systems under limited temporal resolution.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In many real-world scenarios, such as single-cell RNA sequencing, data are observed only as discrete-time snapshots spanning finite time intervals and subject to noisy timestamps, with no continuous trajectories available. Recovering the underlying continuous-time dynamics from these snapshots with coarse and noisy observation times is a critical and challenging task. We propose Continuous-Time Optimal Transport Flow (CT-OT Flow), which first infers high-resolution time labels via partial optimal transport and then reconstructs a continuous-time data distribution through a temporal kernel smoothing. This reconstruction enables accurate training of dynamics models such as ODEs and SDEs. CT-OT Flow consistently outperforms state-of-the-art methods on synthetic benchmarks and achieves lower reconstruction errors on real scRNA-seq and typhoon-track datasets. Our results highlight the benefits of explicitly modeling temporal discretization and timestamp uncertainty, offering an accurate and general framework for bridging discrete snapshots and continuous-time processes.

Problem

• Recovering continuous-time dynamics from noisy discrete snapshots
• Inferring high-resolution time labels from coarse observations
• Bridging discrete snapshots and continuous processes accurately

Innovation

• Estimates continuous-time dynamics from discrete snapshots
• Uses partial optimal transport for time labels
• Reconstructs data distribution with temporal kernel smoothing