Adaptive Sampling for Hydrodynamic Stability

• URL: http://arxiv.org/abs/2512.13532v1
• Date: Mon, 15 Dec 2025 17:00:09 GMT
• Title: Adaptive Sampling for Hydrodynamic Stability
• Authors: Anshima Singh, David J. Silvester,
• Abstract summary: The study extends the machine-learning approach of Silvester (Machine Learning for Hydrodynamic Stability, arXiv:2407.09572)<n>The proposed methodology introduces adaptivity through a flow-based deep generative model that automatically refines the sampling of the parameter space.<n>KRnet is trained to approximate a probability density function that concentrates sampling in regions of high entropy.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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