arXiv subjects

Chenyao Wang

Publications and source records attributed to Chenyao Wang.

4 recordsLinked to original sources

arXiv2026

A Measure-Consistent Operator Learning Method for Infinite-Dimensional Master Equations

Master equations in mean field game theory characterize feedback value functions that depend on time, state (space), and the population distribution. Their numerical approximation is challenging because the unknown is defined on a space of probability measures and the equation involves intrinsic measure derivatives and nonlocal population terms. This paper proposes a measure-consistent operator learning method (MCOL) for infinite-dimensional master equations. The population distribution is represented by an empirical measure and encoded through a symmetric pooling structure, so that the network input is built directly from the particles representing the measure. The same particles are used in the empirical quadrature of the nonlocal residual terms, avoiding additional quadrature grids or auxiliary integration points. A key feature is that the intrinsic derivative appearing in the residual is induced by the same measure-dependent representation that defines the approximation of the value function. Consequently, the value function, its measure derivative, and the empirical residual are tied to a common measure representation, leading to a structurally coupled value-derivative approximation. We also introduce an error decomposition separating neural approximation error from empirical discretization error. Numerical experiments on several master equations show that MCOL accurately approximates the value function, intrinsic measure derivatives, and feedback quantities, and remains robust under changes in the input measures.

math.NA↗

arXiv2026

PINN-Based Kolmogorov-Arnold Networks with RAR-D Adaptive Sampling for Solving Elliptic Interface Problems

Physics-Informed Neural Networks (PINNs) have become a popular and powerful framework for solving partial differential equations (PDEs), leveraging neural networks to approximate solutions while embedding PDE constraints, boundary conditions, and interface jump conditions directly into the loss function. However, most existing PINN approaches are based on multilayer perceptrons (MLPs), which may require large network sizes and extensive training to achieve high accuracy, especially for complex interface problems. In this work, we propose a novel PINN architecture based on Kolmogorov-Arnold Networks (KANs), which offer greater flexibility in choosing activation functions and can represent functions with fewer parameters. Specifically, we introduce a dual KANs structure that couples two KANs across subdomains and explicitly enforces interface conditions. To further boost training efficiency and convergence, we integrate the RAR-D adaptive sampling strategy to dynamically refine training points. Numerical experiments on the elliptic interface problems yield more uniform error distributions across the computational domain, which demonstrates that our PINN-based KANs achieve superior accuracy with significantly smaller network sizes and faster convergence compared to standard PINNs.

math.NA↗

arXiv2023

Hierarchical Dense Correlation Distillation for Few-Shot Segmentation

Few-shot semantic segmentation (FSS) aims to form class-agnostic models segmenting unseen classes with only a handful of annotations. Previous methods limited to the semantic feature and prototype representation suffer from coarse segmentation granularity and train-set overfitting. In this work, we design Hierarchically Decoupled Matching Network (HDMNet) mining pixel-level support correlation based on the transformer architecture. The self-attention modules are used to assist in establishing hierarchical dense features, as a means to accomplish the cascade matching between query and support features. Moreover, we propose a matching module to reduce train-set overfitting and introduce correlation distillation leveraging semantic correspondence from coarse resolution to boost fine-grained segmentation. Our method performs decently in experiments. We achieve $50.0\%$ mIoU on \coco~dataset one-shot setting and $56.0\%$ on five-shot segmentation, respectively.

cs.CV↗

arXiv2020

Modeling, Simulation and Implementation of a Bird-Inspired Morphing Wing Aircraft

We present a design of a bird-inspired morphing wing aircraft, including bionic research, modeling, simulation and flight experiments. Inspired by birds and activated by a planar linkage, our proposed aircraft has three key states: gliding, descending and high-maneuverability. We build the aerodynamic model of the aircraft and analyze its mechanisms to find out a group of optimized parameters. Furthermore, we validate our design by Computational Fluid Dynamics (CFD) simulation based on Lattice-Boltzmann technology and determine three phases of the planar linkage for the three states. Lastly, we manufacture a prototype and conduct flight experiments to test the performance of the aircraft.

eess.SY↗