Delay Embeddings

Delay embedding techniques reconstruct the full state of a dynamical system from observations of only a subset of its variables, leveraging the temporal correlations within the time series data. Current research focuses on applying delay embeddings within machine learning frameworks, particularly deep neural networks and state-space models, to improve prediction accuracy and parameter inference in complex systems, even with noisy or partially observed data. This approach is proving valuable across diverse fields, enabling more accurate modeling of chaotic systems, improved change-point detection in industrial processes, and enhanced signal reconstruction in applications like audio inpainting. The ability to effectively learn and utilize delay embeddings significantly advances our capacity to analyze and model complex, high-dimensional systems from limited data.

Papers

July 8, 2024

Change-Point Detection in Industrial Data Streams based on Online Dynamic Mode Decomposition with Control
Marek Wadinger, Michal Kvasnica, Yoshinobu Kawahara
External Control Data Stream Online Service Change Point Detection Dynamic Mode Decomposition Delay Embeddings

June 17, 2024

Delay Embedding Theory of Neural Sequence Models
Mitchell Ostrow, Adam Eisen, Ila Fiete
Language Model Theoretical Understanding Sequence Model Intermediate Layer Account Time Delay Neural Sequence Model Delay Embeddings

November 20, 2022

Deep learning delay coordinate dynamics for chaotic attractors from partial observable data
Charles D. Young, Michael D. Graham
High Dimensional Dynamical System Discrete Time Chaotic Behavior Chaotic Attractor Delay Embeddings

March 18, 2022

Soft Smoothness for Audio Inpainting Using a Latent Matrix Model in Delay-embedded Space
Tatsuya Yokota
Regularization Model Audio Driven Average Smoothness Variational Regularization Smooth Signal Delay Embeddings Embedded Space

March 11, 2022

Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators
Alex Tong Lin, Adrian S. Wong, Robert Martin, Stanley J. Osher, Daniel Eckhardt
Time Series Dynamical System Handwritten Trajectory Parameter Inference Delay Embeddings

January 13, 2022

Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders
Joseph Bakarji, Kathleen Champion, J. Nathan Kutz, Steven L. Brunton
Nonlinear Dynamic Global Attractor Incomplete Measurement Closed Form Delay Embeddings

Delay Embeddings

Papers

Change-Point Detection in Industrial Data Streams based on Online Dynamic Mode Decomposition with Control

Delay Embedding Theory of Neural Sequence Models

Deep learning delay coordinate dynamics for chaotic attractors from partial observable data

Soft Smoothness for Audio Inpainting Using a Latent Matrix Model in Delay-embedded Space

Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators

Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders