# Modeling Dynamic Mixtures of Time-Delay Systems from Streaming Time Series

arXiv: https://arxiv.org/abs/2605.26191 · HTML: https://mlsanity.com/paper/2605.26191/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 17 of 17)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Learning unknown ODE models with Gaussian processes](https://mlsanity.com/paper/1803.04303/) (2018)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization](https://mlsanity.com/paper/2206.00176/) (2022)
- [Learning Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2201.11211/) (2022)
- [Scalable Variational Inference for Dynamical Systems](https://mlsanity.com/paper/1705.07079/) (2017)
- [Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2307.06538/) (2023)
- [Learning Differential Operators for Interpretable Time Series Modeling](https://mlsanity.com/paper/2209.01491/) (2022)
- [Modeling Time-evolving Causality over Data Streams](https://mlsanity.com/paper/2502.08963/) (2025)
- [Discovering Physics Laws of Dynamical Systems via Invariant Function Learning](https://mlsanity.com/paper/2502.04495/) (2025)
- [Modeling Latent Non-Linear Dynamical System over Time Series](https://mlsanity.com/paper/2412.08114/) (2024)
- [Modeling Regime Shifts in Multiple Time Series](https://mlsanity.com/paper/2109.09692/) (2021)

## Abstract (arXiv)

This research addresses the problem of adaptive modeling in time-series data streams with clear input-output relationships. This problem is challenging because rapid system changes (regime shifts) caused by environmental factors or input delay changes degrade model performance, and the trade-off among accuracy, robustness, and memory usage arises when using multiple small models for each time-series pattern. To address these issues, this paper presents an online framework/method that treats streaming time series as dynamic mixtures of time-delay systems. This framework maintains robustness of model tracking and reduces memory usage by summarizing past regimes using a fixed-length representation that captures both the system dynamics and input-output delays. Concretely, this approach constructs a summary system tensor using the system's Markov parameter series, capturing both dynamic behavior and delay characteristics. If necessary, a tensor decomposition algorithm extracts relevant past models from the tensor and helps select the system that best fits the current regime. This method enables rapid adaptation to environmental changes and is computationally efficient. Tests on real datasets show that DelayMix consistently outperforms other methods, achieving superior forecast accuracy and faster adaptation to delays, especially for highly non-stationary data.