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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Adapformer: Adaptive channel management for multivariate time series forecasting.

Yuchen Luo1, Xinyu Li2, Liuhua Peng1

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This study introduces Adapformer, a novel approach for multivariate time series forecasting (MTSF). Adapformer effectively models complex dependencies, outperforming existing methods in accuracy and efficiency.

Keywords:
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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Time Series Analysis

Background:

  • Multivariate time series forecasting (MTSF) faces challenges in modeling inter-variable dependencies.
  • Existing channel-independent (CI) and channel-dependent (CD) methods have limitations, either ignoring interactions or introducing noise.
  • There is a need for advanced MTSF models that balance capturing dependencies with predictive efficiency.

Purpose of the Study:

  • To introduce the Adaptive Forecasting Transformer (Adapformer), a novel framework for MTSF.
  • To address the limitations of CI and CD approaches by integrating effective channel management.
  • To improve both the accuracy and computational efficiency of multivariate time series forecasting.

Main Methods:

  • Developed Adapformer, a Transformer-based framework with a dual-stage encoder-decoder architecture.
  • Introduced the Adaptive Channel Enhancer (ACE) to enrich token representations by selectively incorporating dependencies.
  • Implemented the Adaptive Channel Forecaster (ACF) to refine predictions by focusing on relevant covariates, reducing noise.

Main Results:

  • Adapformer demonstrated superior performance compared to existing MTSF models across diverse datasets.
  • The proposed model achieved enhanced predictive accuracy.
  • Significant improvements in computational efficiency were observed with Adapformer.

Conclusions:

  • Adapformer offers a state-of-the-art solution for MTSF by effectively managing channel dependencies.
  • The framework successfully merges the benefits of CI and CD strategies.
  • Adapformer represents a significant advancement in accurate and efficient multivariate time series forecasting.