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Rapidly Varying Flow01:24

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Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...
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The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
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Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed slope, channel shape variations, or obstructions. This flow type occurs when the depth adjusts gradually to balance gravitational forces, shear forces, and energy requirements, resulting in a low rate of depth change.Characteristics of Gradually Varying FlowGVF is commonly observed in natural streams, rivers, and canals, where flow depth...
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A Quasi-Monte Carlo Method Based on Neural Autoregressive Flow.

Yunfan Wei1, Wei Xi2

  • 1School of Mathematics, South China University of Technology, Guangzhou 510641, China.

Entropy (Basel, Switzerland)
|September 27, 2025
PubMed
Summary

This study introduces a transport quasi-Monte Carlo (TQMC) framework using neural autoregressive flows for efficient high-dimensional sampling and integration. TQMC improves accuracy and predictive performance in financial modeling.

Keywords:
autoregressive modelnormalizing flowquasi-Monte Carlostock return predictiontransport map

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Area of Science:

  • Computational Statistics
  • Machine Learning
  • Financial Mathematics

Background:

  • High-dimensional integration and sampling are computationally intensive.
  • Existing methods like standard Monte Carlo and normalizing flows have limitations in efficiency and accuracy.
  • Approximating complex probability distributions is crucial for various scientific and financial applications.

Purpose of the Study:

  • To develop a novel transport quasi-Monte Carlo (TQMC) framework for efficient sampling and integration.
  • To combine randomized quasi-Monte Carlo sampling with neural autoregressive flows.
  • To demonstrate the framework's superior performance over existing methods in accuracy and efficiency.

Main Methods:

  • A sequence of invertible transport maps is constructed to approximate target densities.
  • The approximation is achieved by decomposing complex distributions into lower-dimensional marginals.
  • Normalizing flows parameterized via monotonic beta-averaging transformations are utilized, optimized with forward Kullback-Leibler divergence.
  • A hidden-variable mechanism transfers parameters between sub-models for enhanced computational efficiency.

Main Results:

  • Numerical experiments on a banana-shaped distribution show TQMC outperforms standard Monte Carlo-based normalizing flows in sampling accuracy and integral estimation.
  • Application to A-share stock return data demonstrates reliable predictive performance in semiannual return forecasts.
  • The model accurately captures covariance structures across assets, indicating its utility in financial modeling.

Conclusions:

  • The proposed transport quasi-Monte Carlo framework offers significant improvements in sampling and integration efficiency and accuracy.
  • TQMC shows strong potential for application in financial modeling, particularly in return forecasting and covariance estimation.
  • This novel approach advances the field of high-dimensional inference and statistical modeling.