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[2512.13532] Adaptive Sampling for Hydrodynamic Stability
Summary
This article presents an adaptive sampling method for efficiently detecting bifurcation boundaries in fluid flow problems, enhancing the use of machine learning in hydrodynamic stability analysis.
Why It Matters
The research addresses a significant challenge in fluid dynamics by improving the identification of bifurcation boundaries, which is crucial for understanding flow stability. The integration of machine learning techniques can lead to more efficient simulations, reducing computational costs while maintaining accuracy, thereby advancing both theoretical and practical applications in fluid dynamics.
Key Takeaways
- Introduces an adaptive sampling approach for bifurcation detection in fluid dynamics.
- Combines a classifier network with a generative model to refine parameter space sampling.
- Achieves accurate results with fewer simulations compared to traditional methods.
- Utilizes Shannon entropy as an uncertainty indicator for flow stability.
- Establishes a scalable framework for high-dimensional stability analysis.
Physics > Fluid Dynamics arXiv:2512.13532 (physics) [Submitted on 15 Dec 2025 (v1), last revised 18 Feb 2026 (this version, v2)] Title:Adaptive Sampling for Hydrodynamic Stability Authors:Anshima Singh, David J. Silvester View a PDF of the paper titled Adaptive Sampling for Hydrodynamic Stability, by Anshima Singh and David J. Silvester View PDF HTML (experimental) 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~(J. Comput. Phys., 553 (2026), 114743), 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 coup...