arXiv subjects

Yutian He

Publications and source records attributed to Yutian He.

4 recordsLinked to original sources

arXiv2026

Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel optimization and minimax optimization separately, existing methods mainly focus on bilevel optimization with lower-level minimization problems, often under strong convexity assumptions, and are not directly applicable to the minimax lower-level setting considered here. To address this gap, we develop penalty-based first-order methods for bilevel minimax optimization without requiring strong convexity of the lower-level problem. In the deterministic setting, we establish that the proposed method finds an $\epsilon$-KKT point with $\tilde{O}(\epsilon^{-4})$ oracle complexity. We further show that bilevel problems with convex constrained lower-level minimization can be reformulated as special cases of our framework via Lagrangian duality, leading to an $\tilde{O}(\epsilon^{-4})$ complexity bound that improves upon the existing $\tilde{O}(\epsilon^{-7})$ result. Finally, we extend our approach to the stochastic setting, where only stochastic gradient oracles are available, and prove that the proposed stochastic method finds a nearly $\epsilon$-KKT point with $\tilde{O}(\epsilon^{-9})$ oracle complexity.

math.OC↗

arXiv2025

Confinement geometry governs the impact of external shear stress on active stress-driven flows in microtubule-kinesin active fluids

Active fluids generate internal active stress and exhibit unique responses to external forces such as superfluidity and self-yielding transitions. However, how confinement geometry influences these responses remains poorly understood. Here, we investigate microtubule-kinesin active fluids under external shear stresses in two geometries. In slab-like confinement (a narrow-gap cavity), external stresses propagated throughout the system, leading to stress competition and a kinematic transition that shifted dynamics from active stress-dominated to shear stress-dominated flow. At the transition, we estimate the active stress to be ~1.5 mPa. Simulation supported that this transition arises from stress competition. In contrast, in ring-like confinement (a toroidal system), external forces acted locally, inducing a mini cavity flow that triggered self-organized reconfiguration rather than direct entrainment. These findings show that the response of active fluids to external forcing depends not only on the magnitude of the applied stress but also on how confinement geometry directs and redistributes that stress, revealing a new approach to controlling active fluid behavior by combining static geometrical design with dynamic external stimuli for real-time modulation of flow patterns. Such control strategies may be applied to microfluidic systems, where external inputs such as micromechanical actuators can dynamically tune active fluid behavior within fixed device geometries, enabling transitions between chaotic and coherent flows for tasks such as mixing, sorting, or directed transport.

cond-mat.soft↗

arXiv2025

A three-dimensional scanning stereoscopic particle image velocimetry for large-volume liquid flows

We introduce a Scanning Stereoscopic Particle Image velocimetry~(SSPIV) system which incorporates a thin rotating prism to obtain three-dimensional velocity fields in a large cubical measurement volume. The system makes use of an arrangement where a laser beam is first laterally deflected using an even-faced prism, and then passed through a cylindrical lens rod to obtain light sheets for illumination. This eliminates the need for large rotating mirrors or heavy prisms and facilitates relatively fast rotation speeds of up to 4800 rpm for the prism, yielding three-dimensional, three-component velocity field over a large depth at relatively high particle seeding density. About $10^6$ velocity vectors (3D-3C) are obtained in a single volumetric-scan of $100 \times 100 \times 100$ mm$^3$. The method is demonstrated using two independent experiments, (1) a round jet at Reynolds number Re = 1000, and (2) the flow field around a freely rising sphere at a Reynolds number Re$_p$ $\approx$ 260, and the wake flow is compared with direct numerical simulations of a falling viscous droplet. The scanning gives time-resolved evolution of the large-scale vortical structures of the Re = 1000 jet, with spatial gradients captured fairly well. The three-dimensional flow field surrounding the refractive-index-matched rising sphere is shown to be steady and non-axisymmetric. The flow field and separation bubble are seen to be similar, but slightly shorter than that of the falling droplet case and the uniform flow past a fixed sphere case at a comparable Reynolds number.

physics.flu-dyn↗

arXiv2025

Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints

Fairness in machine learning has become a critical concern. Existing approaches often focus on achieving full fairness across all score ranges generated by predictive models, ensuring fairness in both high- and low-percentile populations. However, this stringent requirement can compromise predictive performance and may not align with the practical fairness concerns of stakeholders. In this work, we propose a novel framework for building partially fair machine learning models that enforce fairness only within a specific percentile interval of interest while maintaining flexibility in other regions. We introduce statistical metrics to evaluate partial fairness within a given percentile interval. To achieve partial fairness, we propose an in-processing method by formulating the model training problem as constrained optimization with difference-of-convex constraints, which can be solved by an inexact difference-of-convex algorithm (IDCA). We provide the complexity analysis of IDCA for finding a nearly KKT point. Through numerical experiments on real-world datasets, we demonstrate that our framework achieves high predictive performance while enforcing partial fairness where it matters most.

cs.LG↗