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Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
Uniform Depth Channel Flow01:27

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Rapidly Varying Flow01:24

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Gradually Varying Flow01:29

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Updated: Jun 6, 2026

A Microfluidic Model of Biomimetically Breathing Pulmonary Acinar Airways
09:39

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Published on: May 9, 2016

Flow-Matching Posterior Sampling: A Training-Free Conditional Generation for Flow Matching.

Kaiyu Song, Hanjiang Lai, Yan Pan

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |June 4, 2026
    PubMed
    Summary
    This summary is machine-generated.

    Flow Matching-based Posterior Sampling (FMPS) enables training-free conditional generation by adapting flow matching models. This novel approach introduces a correction term, allowing for posterior sampling without retraining and improving generation quality.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Computer Vision

    Background:

    • Training-free conditional generation leverages pre-trained models without retraining.
    • Existing methods like posterior sampling require score functions, which flow matching models lack.
    • Prior approximate posterior sampling for flow matching is limited to linear problems.

    Purpose of the Study:

    • To introduce Flow Matching-based Posterior Sampling (FMPS) for broader application in conditional generation.
    • To enable posterior sampling within the flow matching framework.
    • To improve generation quality and computational efficiency in training-free conditional generation.

    Main Methods:

    • Proposed FMPS by introducing a correction term to steer the velocity field.
    • Reformulated the correction term to incorporate a surrogate score function.
    • Developed two practical implementations for generation quality and computational efficiency.

    Main Results:

    • FMPS successfully enables posterior sampling in flow matching models.
    • The proposed correction mechanism bridges the gap between flow matching and score-based posterior sampling.
    • Experimental results show superior generation quality compared to state-of-the-art methods.

    Conclusions:

    • FMPS is an effective and generalizable method for training-free conditional generation.
    • The approach broadens the applicability of posterior sampling to flow matching models.
    • FMPS offers improvements in both generation quality and computational efficiency.