{"ID":2829061,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.13532","arxiv_id":"2512.13532","title":"Adaptive Sampling for Hydrodynamic Stability","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 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.","short_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...","url_abs":"https://arxiv.org/abs/2512.13532","url_pdf":"https://arxiv.org/pdf/2512.13532v2","authors":"[\"Anshima Singh\",\"David J. Silvester\"]","published":"2025-12-15T17:00:09Z","proceeding":"physics.flu-dyn","tasks":"[\"physics.flu-dyn\",\"cs.LG\"]","methods":"[]","has_code":false}