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Related Experiment Video

Updated: Jun 23, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Controlled Differential Equations on Long Sequences via Non-standard Wavelets.

Sourav Pal1, Zhanpeng Zeng1, Sathya N Ravi2

  • 1University of Wisconsin-Madison.

Proceedings of Machine Learning Research
|June 17, 2024
PubMed
Summary
This summary is machine-generated.

Neural Controlled Differential Equations (NCDEs) are improved for long sequences using an integral transform and wavelet decomposition. This simplification enhances modeling for regression, classification, and coupled differential equations.

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Area of Science:

  • Machine Learning
  • Dynamical Systems
  • Signal Processing

Background:

  • Neural Controlled Differential Equations (NCDEs) model complex temporal dynamics but struggle with long sequences.
  • Existing methods using log signatures lack invertibility, limiting applications like reconstruction and generative modeling.

Purpose of the Study:

  • To develop an efficient simplification of NCDEs for fixed-length temporal sequences.
  • To enhance the scope of problems addressable by NCDEs, including those requiring model invertibility.

Main Methods:

  • Recasting regression/classification tasks as integral transforms.
  • Restricting operator classes to enable decomposition using non-standard wavelets.
  • Developing a neural variant of the simplified operator learning approach.

Main Results:

  • Demonstrated consistent improvements across various use cases tackled by existing NCDE methods.
  • Successfully applied the novel approach to modeling tasks involving coupled differential equations.
  • The simplification radically reduces the complexity of learning the operator.

Conclusions:

  • The proposed integral transform and wavelet-based simplification offers an efficient and effective alternative for NCDEs on fixed-length sequences.
  • This approach broadens the applicability of NCDEs, particularly for tasks requiring model invertibility and for modeling coupled systems.