arXiv subjects

Qiao Zhuang

Publications and source records attributed to Qiao Zhuang.

7 recordsLinked to original sources

arXiv2026

Carleman Estimates for Wave Equations on the Half-Line: AI-Assisted Weights and Applications

We develop an AI-assisted search-and-certification workflow for constructing Carleman weights for wave equations on semi-infinite domains. Starting from a weighted cross-term identity used to derive the Carleman estimate, we derive explicit analytical screening conditions and use an AI system to propose symbolic candidate weights subject to those conditions. The search identifies a logarithmic weight structure with concrete parameter values; the subsequent human verification by the authors then retains this structure, derives the admissible parameter range, and rigorously certifies the selected weight by verifying the required quantitative conditions. Based on the identified and certified Carleman weight, the subsequent proofs, analysis, and applications are carried out entirely by the authors: we establish a global Carleman estimate for the wave operator on the half-line and derive a weighted conditional lateral Cauchy stability result. The proposed weight is further used in a finite-depth one-sided reconstruction problem for semilinear wave equations on the half-line, where the initial-time flux induces an endpoint graph stabilizer and a contractive frozen nonlinear reconstruction map. Numerical experiments support the predicted contraction behavior and show improved robustness to noisy data from the Carleman weighting, with the induced endpoint graph term providing further stabilization at higher noise levels.

math.AP↗

arXiv2026

Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters

We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale parameter defined as the geometric mean of all parameters. We thus augment the network input with a scale-aware feature, enabling it to capture sharp solution transitions intrinsically. Numerical experiments across a range of dynamical systems demonstrate that the proposed framework can handle coupled systems with multiple and high-contrast small parameters and obtain satisfactory accuracy in capturing solution features induced by small parameters.

math.NA↗

arXiv2026

On-the-Fly VLA Adaptation via Test-Time Reinforcement Learning

Vision-Language-Action models have recently emerged as a powerful paradigm for general-purpose robot learning, enabling agents to map visual observations and natural-language instructions into executable robotic actions. Though popular, they are primarily trained via supervised fine-tuning or training-time reinforcement learning, requiring explicit fine-tuning phases, human interventions, or controlled data collection. Consequently, existing methods remain unsuitable for challenging simulated- or physical-world deployments, where robots must respond autonomously and flexibly to evolving environments. To address this limitation, we introduce a Test-Time Reinforcement Learning for VLAs (TT-VLA), a framework that enables on-the-fly policy adaptation during inference. TT-VLA formulates a dense reward mechanism that leverages step-by-step task-progress signals to refine action policies during test time while preserving the SFT/RL-trained priors, making it an effective supplement to current VLA models. Empirical results show that our approach enhances overall adaptability, stability, and task success in dynamic, previously unseen scenarios under simulated and real-world settings. We believe TT-VLA offers a principled step toward self-improving, deployment-ready VLAs.

cs.RO↗

arXiv2025

PAS-Net: Physics-informed Adaptive Scale Deep Operator Network

Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-informed Adaptive-Scale Deep Operator Network for learning solution operators of nonlinear and singularly perturbed evolution PDEs with small parameters and localized features. Specifically, PAS-Net augments the trunk input in the physics informed Deep Operator Network (PI-DeepONet) with a prescribed (or learnable) locally rescaled coordinate transformation centered at reference points. This addition introduces a multiscale feature embedding that acts as an architecture-independent preconditioner which improves the representation of localized, stiff, and multiscale dynamics. From an optimization perspective, the adaptive-scale embedding in PAS-Net modifies the geometry of the Neural Tangent Kernel (NTK) associated with the neural network by increasing its smallest eigenvalue, which in turn improves spectral conditioning and accelerates gradient-based convergence. We further show that this adaptive-scale mechanism explicitly accelerates neural network training in approximating functions with steep transitions and strong asymptotic behavior, and we provide a rigorous proof of this function-approximation result within the finite-dimensional NTK matrix framework. We test the proposed PAS-Net on three different problems: (i) the one-dimensional viscous Burgers equation, (ii) a nonlinear diffusion-reaction system with sharp spatial gradients, and (iii) a two-dimensional eikonal equation. The numerical results show that PAS-Net consistently achieves higher accuracy and faster convergence than the standard DeepONet and PI-DeepONet models under a similar training cost.

physics.comp-ph↗

arXiv2024

Two-scale Neural Networks for Partial Differential Equations with Small Parameters

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of neural networks. The proposed method enables solving PDEs with small parameters in a simple fashion, without adding Fourier features or other computationally taxing searches of truncation parameters. Various numerical examples demonstrate reasonable accuracy in capturing features of large derivatives in the solutions caused by small parameters.

math.NA↗

arXiv2021

Symmetry-Protected Topological relationship between $SU(3)$ and $SU(2)\times{U(1)}$ in Two Dimension

Symmetry-protected topological $\left(SPT\right)$ phases are gapped short-range entangled states with symmetry $G$, which can be systematically described by group cohomology theory. $SU(3)$ and $SU(2)\times{U(1)}$ are considered as the basic groups of Quantum Chromodynamics and Weak-Electromagnetic unification, respectively. In two dimension $(2D)$, nonlinear-sigma models with a quantized topological Theta term can be used to describe nontrivial SPT phases. By coupling the system to a probe field and integrating out the group variables, the Theta term becomes the effective action of Chern-Simons theory which can derive the response current density. As a result, the current shows a spin Hall effect, and the quantized number of the spin Hall conductance of SPT phases $SU(3)$ and $SU(2)\times{U(1)}$ are same. In addition, relationships between $SU(3)$ and $SU(2)\times{U(1)}$ which maps $SU(3)$ to $SU(2)$ with a rotation $U(1)$ will be given.

cond-mat.other↗

arXiv2020

Error Analysis of Symmetric Linear/Bilinear Partially Penalized Immersed Finite Element Methods for Helmholtz Interface Problems

This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations. Under the assumption that the exact solution possesses a usual piecewise $H^2$ regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual $L^2$ norm provided that the mesh size is sufficiently small. A numerical example is conducted to validate the theoretical conclusions.

math.NA↗