Trajectory Flow Matching with Applications to Clinical Time Series Modeling

TL;DR

This paper introduces Trajectory Flow Matching (TFM), a scalable and stable method for training Neural SDEs without backpropagation through dynamics, improving modeling of irregular clinical time series.

Contribution

The paper proposes TFM, a novel simulation-free training method for Neural SDEs, with theoretical conditions and a reparameterization trick, tailored for clinical time series.

Findings

TFM improves training stability and scalability.

Enhanced performance on clinical datasets.

Better uncertainty prediction in time series modeling.

Abstract

Modeling stochastic and irregularly sampled time series is a challenging problem found in a wide range of applications, especially in medicine. Neural stochastic differential equations (Neural SDEs) are an attractive modeling technique for this problem, which parameterize the drift and diffusion terms of an SDE with neural networks. However, current algorithms for training Neural SDEs require backpropagation through the SDE dynamics, greatly limiting their scalability and stability. To address this, we propose Trajectory Flow Matching (TFM), which trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. TFM leverages the flow matching technique from generative modeling to model time series. In this work we first establish necessary conditions for TFM to learn time series data. Next, we present a reparameterization trick which improves training stability. Finally, we adapt TFM to the clinical time series setting, demonstrating improved performance on three clinical time series datasets both in terms of absolute performance and uncertainty prediction.