Time-series modeling with neural flow maps

Constructing mathematical models from data is fundamental for understanding complex systems across scientific disciplines. However, real-world data often pose challenges such as irregular sampling, sparsity, and noise, that hinder the development of accurate, mechanistic models. In this work, we present a deep learning framework that directly reconstruct flow maps from data, assuming only that the observed patterns arise from an autonomous dynamical system. We demonstrate that our method accurately captures system dynamics across diverse settings, even with limited and irregularly sampled training data. When applied to the circadian transcriptomic time series data, it generates biologically valid predictions by integrating information across multiple organs. By parameterizing the full dynamical system, our proposed approach enables efficient computation of time derivatives and Jacobians directly from data, offering a powerful tool for analyzing and interpreting high-dimensional biological systems.