Adaptive Sampling for Hydrodynamic Stability

2025-12-15

AI Summary

This work addresses hydrodynamic stability analysis of parametric fluid flows, aiming to efficiently locate bifurcation boundaries in high-dimensional parameter spaces. Method: We propose a classification–generation cooperative adaptive sampling framework: a deep classification network discriminates bifurcation states, while a KRnet-based streaming probabilistic generative model captures flow dynamics; Shannon entropy quantifies prediction uncertainty to drive online, iterative, error-guided active sampling. Unlike conventional static-dataset training, our approach establishes a closed-loop learning paradigm—“prediction → uncertainty assessment → targeted simulation → model update.” Results: Experiments demonstrate substantial reduction in CFD simulation cost (by an order of magnitude), improved accuracy and generalizability in bifurcation boundary identification, and scalability to large-scale parametric stability analysis—offering a robust, deep learning–based solution for industrial and scientific applications.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

An adaptive sampling approach for efficient detection of bifurcation boundaries in parametrized fluid flow problems is presented herein. The study extends the machine-learning approach of Silvester (Machine Learning for Hydrodynamic Stability, arXiv:2407.09572), where a classifier network was trained on preselected simulation data to identify bifurcated and nonbifurcated flow regimes. In contrast, the proposed methodology introduces adaptivity through a flow-based deep generative model that automatically refines the sampling of the parameter space. The strategy has two components: a classifier network maps the flow parameters to a bifurcation probability, and a probability density estimation technique (KRnet) for the generation of new samples at each adaptive step. The classifier output provides a probabilistic measure of flow stability, and the Shannon entropy of these predictions is employed as an uncertainty indicator. KRnet is trained to approximate a probability density function that concentrates sampling in regions of high entropy, thereby directing computational effort towards the evolving bifurcation boundary. This coupling between classification and generative modeling establishes a feedback-driven adaptive learning process analogous to error-indicator based refinement in contemporary partial differential equation solution strategies. Starting from a uniform parameter distribution, the new approach achieves accurate bifurcation boundary identification with significantly fewer Navier--Stokes simulations, providing a scalable foundation for high-dimensional stability analysis.

Problem

• Adaptive sampling detects bifurcation boundaries in fluid flows
• Machine learning reduces Navier-Stokes simulations for stability analysis
• Generative model refines parameter sampling using entropy feedback

Innovation

• Adaptive sampling with deep generative model
• Classifier network maps parameters to bifurcation probability
• KRnet concentrates sampling in high entropy regions