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

Published version (preferred citation): Proceedings of the AAAI Conference on Artificial Intelligence, vol. 40, no. 29, pp. 24594-24603, 2026. Official page · DOI: 10.1609/aaai.v40i29.39643

arXiv preprint: arXiv:2511.10841, DOI: 10.48550/arXiv.2511.10841

Authors: YongKyung Oh, Dong-Young Lim, Sungil Kim

TL;DR: FlowPath is a learnable control path for neural controlled differential equations (Neural CDEs). Instead of a fixed interpolation, it uses invertible neural flows to learn a continuous, data-driven manifold for robust irregular time series classification, even under heavy missingness.

Keywords: Machine Learning: ML: Time-Series/Data Streams, Machine Learning: ML: Deep Learning Algorithms, Machine Learning: ML: Representation Learning, Machine Learning: ML: Learning with Manifolds

Overview

Modeling continuous-time dynamics from sparse, irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations offer a principled framework, but their performance is highly sensitive to how discrete observations are lifted into continuous control paths. Most existing models rely on fixed interpolation schemes that impose simplistic geometric assumptions and often distort the data manifold, especially under high missingness.

FlowPath is a learnable path construction method built on invertible neural flows. Instead of linking observations through a predefined interpolant, it learns a continuous, data-adaptive manifold subject to invertibility constraints that promote information-preserving and stable transformations. This inductive bias separates FlowPath from prior unconstrained learnable path models. On benchmark datasets and a real-world case study, FlowPath improves classification accuracy over fixed interpolants and non-invertible architectures, showing the value of modeling both the dynamics along the path and the geometry of the path itself.

Method

FlowPath extends Neural Differential Equation frameworks through:

• Invertible path construction: data-adaptive path via invertible flows.
• Geometry-aware control paths: continuous paths that better reflect the latent manifold than fixed interpolants.
• NCDE compatibility: the learned path plugs into NCDE backbones.

Code architecture

• torch-ists/: utilities and differential-equation models for irregular TS.
• PAMAP2/: human activity recognition and the sensor-drop experiment.

Citation

If you use this software or method, please cite the published AAAI paper:

@article{oh_flowpath_2026,
  title   = {FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classification},
  author  = {Oh, YongKyung and Lim, Dong-Young and Kim, Sungil},
  journal = {Proceedings of the AAAI Conference on Artificial Intelligence},
  volume  = {40},
  number  = {29},
  pages   = {24594--24603},
  year    = {2026},
  doi     = {10.1609/aaai.v40i29.39643},
  url     = {https://ojs.aaai.org/index.php/AAAI/article/view/39643}
}

@misc{oh_flowpath_2025,
  title     = {FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classification},
  author    = {Oh, YongKyung and Lim, Dong-Young and Kim, Sungil},
  year      = {2025},
  publisher = {arXiv},
  doi       = {10.48550/arXiv.2511.10841},
  url       = {https://arxiv.org/abs/2511.10841}
}

A machine-readable citation is also provided in CITATION.cff.

License

Released under the MIT License.