Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Turbulence Regression

Yingang Fan, Binjie Ding, Baiyi Chen

TL;DR

The paper targets turbulence prediction from sparse, continuous 3D wind field data by introducing a discretization-driven NeuTucker framework that leverages a four-dimensional Tucker interaction tensor to model complex spatiotemporal dependencies. It discretizes continuous inputs, embeds them, and uses a Tucker-based factorization to capture high-order interactions among altitude and wind components, with the Richardson Number guiding turbulence diagnostics. Empirical results show the discretized NeuTucker model substantially outperforms baseline regression approaches in missing-observation scenarios, highlighting the value of discrete representation and four-dimensional tensor modeling for turbulence analysis. The work advances practical turbulence prediction in meteorology and aviation by enabling robust tensor-based regression on incomplete wind-field data and suggests avenues for broader application and refinement.

Abstract

Air turbulence refers to the disordered and irregular motion state generated by drastic changes in velocity, pressure, or direction during airflow. Various complex factors lead to intricate low-altitude turbulence outcomes. Under current observational conditions, especially when using only wind profile radar data, traditional methods struggle to accurately predict turbulence states. Therefore, this paper introduces a NeuTucker decomposition model utilizing discretized data. Designed for continuous yet sparse three-dimensional wind field data, it constructs a low-rank Tucker decomposition model based on a Tucker neural network to capture the latent interactions within the three-dimensional wind field data. Therefore, two core ideas are proposed here: 1) Discretizing continuous input data to adapt to models like NeuTucF that require discrete data inputs. 2) Constructing a four-dimensional Tucker interaction tensor to represent all possible spatio-temporal interactions among different elevations and three-dimensional wind speeds. In estimating missing observations in real datasets, this discretized NeuTucF model demonstrates superior performance compared to various common regression models.

Turbulence Regression

TL;DR

The paper targets turbulence prediction from sparse, continuous 3D wind field data by introducing a discretization-driven NeuTucker framework that leverages a four-dimensional Tucker interaction tensor to model complex spatiotemporal dependencies. It discretizes continuous inputs, embeds them, and uses a Tucker-based factorization to capture high-order interactions among altitude and wind components, with the Richardson Number guiding turbulence diagnostics. Empirical results show the discretized NeuTucker model substantially outperforms baseline regression approaches in missing-observation scenarios, highlighting the value of discrete representation and four-dimensional tensor modeling for turbulence analysis. The work advances practical turbulence prediction in meteorology and aviation by enabling robust tensor-based regression on incomplete wind-field data and suggests avenues for broader application and refinement.

Abstract

Air turbulence refers to the disordered and irregular motion state generated by drastic changes in velocity, pressure, or direction during airflow. Various complex factors lead to intricate low-altitude turbulence outcomes. Under current observational conditions, especially when using only wind profile radar data, traditional methods struggle to accurately predict turbulence states. Therefore, this paper introduces a NeuTucker decomposition model utilizing discretized data. Designed for continuous yet sparse three-dimensional wind field data, it constructs a low-rank Tucker decomposition model based on a Tucker neural network to capture the latent interactions within the three-dimensional wind field data. Therefore, two core ideas are proposed here: 1) Discretizing continuous input data to adapt to models like NeuTucF that require discrete data inputs. 2) Constructing a four-dimensional Tucker interaction tensor to represent all possible spatio-temporal interactions among different elevations and three-dimensional wind speeds. In estimating missing observations in real datasets, this discretized NeuTucF model demonstrates superior performance compared to various common regression models.

Paper Structure

This paper contains 13 sections, 11 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Richardson Number
  4. Discretization
  5. Tensor and Discretized Tensor
  6. Turbulence Regression
  7. Data Processing
  8. Neural Tucker Factorization
  9. Regression Prediction
  10. Empirical Studies
  11. General Setting
  12. Performance Evaluation
  13. Conclusion

Figures (2)

  • Figure 1: Process of continuous vector discretization, where features within the same value-segmented interval are mapped to an identical integer label
  • Figure 2: An illustration of the discrete Tucker decomposition process of a four-dimensional continuous tensor.

Theorems & Definitions (3)

  • Definition 1: Discretized Vector
  • Definition 2: Mode-4 Tensor
  • Definition 3: Discretized Tensor