FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classification

TL;DR

FlowPath introduces an invertible neural flow to learn data-adaptive control paths, improving the modeling of irregularly-sampled time series for classification tasks.

Contribution

It proposes a novel invertible flow-based method to learn the geometry of control paths, enhancing continuous-time dynamics modeling from sparse data.

Findings

FlowPath outperforms baselines on 18 benchmark datasets.

It achieves statistically significant accuracy improvements.

The method effectively models the geometry of control paths.

Abstract

Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly sensitive to the choice of control path constructed from discrete observations. Existing methods commonly employ fixed interpolation schemes, which impose simplistic geometric assumptions that often misrepresent the underlying data manifold, particularly under high missingness. We propose FlowPath, a novel approach that learns the geometry of the control path via an invertible neural flow. Rather than merely connecting observations, FlowPath constructs a continuous and data-adaptive manifold, guided by invertibility constraints that enforce information-preserving and well-behaved transformations. This inductive bias distinguishes FlowPath from prior unconstrained learnable path models. Empirical evaluations on 18 benchmark datasets and a real-world case study demonstrate that FlowPath consistently achieves statistically significant improvements in classification accuracy over baselines using fixed interpolants or non-invertible architectures. These results highlight the importance of modeling not only the dynamics along the path but also the geometry of the path itself, offering a robust and generalizable solution for learning from irregular time series.