arXiv subjects

Zhaoxiang Li

Publications and source records attributed to Zhaoxiang Li.

9 recordsLinked to original sources

arXiv2026

CARE-SAV: A Conditioning-Aware Random-Feature Framework for Energy-Stable Simulation of Gradient Flows

Gradient-flow models are characterized by an intrinsic energy-dissipation structure, and faithfully preserving this structure at the discrete level is important for stable and reliable long-time simulation. To this end, we develop a Conditioning-Aware Representation Enhancement with Scalar Auxiliary Variable (CARE-SAV) framework, which constructs a compact spatial approximation space from flexible candidate features and evolves the gradient-flow dynamics directly within this space. The resulting fully discrete scheme preserves the discrete energy-dissipation law while providing a flexible alternative to conventional prescribed spatial discretizations. Rigorous analysis establishes the approximation capability, solvability, stability and convergence of the proposed method. Numerical experiments on representative gradient-flow problems demonstrate its accuracy, robustness and computational efficiency. We believe that CARE-SAV could provide a simple, flexible, and computationally efficient paradigm for structure-preserving discretization of gradient-flow problems.

math.NA↗

arXiv2026

PEAfowl: Perception-Enhanced Multi-View Vision-Language-Action for Bimanual Manipulation

Bimanual manipulation in cluttered scenes requires policies that remain stable under occlusions, viewpoint changes and scene variations. Existing vision-language-action models often lack such robustness because (i) multi-view features are fused via view-agnostic token concatenation, yielding limited cross-view spatial representations, and (ii) language is injected as global conditioning, resulting in coarse instruction grounding. In this paper, we introduce PEAfowl, a perception-enhanced multi-view VLA policy for bimanual manipulation. For spatial perception, PEAfowl predicts per-token depth distributions, performs differentiable 3D lifting, and aggregates local cross-view neighbors to form geometrically grounded, cross-view aligned representations. For language utilization, we propose to replace global conditioning with a Perceiver-style text-aware readout over frozen CLIP visual features, enabling iterative evidence accumulation. To better exploit commodity RGB-D sensing despite noisy and incomplete depth, PEAfowl's depth-distribution lifting naturally supports training-only depth distillation, where a pretrained depth teacher supervises the depth-distribution head to inject refined geometric priors without adding inference overhead. On RoboTwin 2.0 under domain-randomized setting, PEAfowl improves the strongest baseline by 23.0 pp in success rate, and physical experiments further demonstrate improved performance on the evaluated real-robot tasks. Project website: https://peafowlvla.github.io/.

cs.CV↗

arXiv2026

PressMimic: Pressure-Guided Motion Capture and Control for Humanoid Robot Imitation

Humanoid motion imitation requires not only accurate perception of human kinematics but also faithful reproduction of physical interactions with the environment. However, existing pipelines rely primarily on vision-based motion capture and kinematic imitation, largely ignoring contact dynamics, leading to artifacts such as foot sliding, floor penetration, and unstable behaviors. In this work, we revisit humanoid motion imitation from the perspective of physical grounding and leverage pressure as a unified modality across perception and control. We present PressMimic, a framework that integrates pressure into the full pipeline from motion capture to humanoid control. In the perception stage, we introduce FRAPPE++, a multimodal model that fuses RGB and pressure to jointly estimate 3D pose and global motion, where pressure provides explicit contact and support constraints to resolve ambiguity in vision-based estimation. In the control stage, we propose a pressure-supervised policy (PSP) that incorporates pressure-derived signals into reinforcement learning, enabling physically consistent contact patterns during execution. We further construct MotionPRO, a large-scale dataset with synchronized RGB, pressure, and motion capture data. Experiments show that pressure improves motion estimation accuracy, trajectory consistency, and execution stability. These results demonstrate that pressure serves as an effective physical grounding signal, bridging perception and control for physically consistent humanoid motion imitation.

cs.RO↗

arXiv2026

C-PINN: A neural network framework based on the Cordès condition for solving linear and fully nonlinear equations in non-divergence form and its applications

In this paper, we propose a novel Physics-Informed Neural Network (PINN) framework based on the Cordès condition for solving both linear and fully nonlinear partial differential equations (PDEs) in non-divergence form, together with their applications. By incorporating the operator structure into the loss function, the proposed method improves the conditioning of the associated optimization problem, thereby enhancing training stability and solution accuracy. The framework is further extended to include Hamilton-Jacobi-Bellman and Monge-Ampère equations, with applications to optimal transport. Numerical experiments demonstrate the effectiveness and robustness of the method, as well as its capability to address high-dimensional problems, highlighting the promise of learning-based approaches for tackling challenging PDEs. Owing to its generality and simplicity, the proposed method is expected to be of broad interest to the scientific and engineering communities.

math.NA↗

arXiv2026

Reconfiguration graphs of $K_{2,3}$-minor-free graphs

The $\ell$-reconfiguration graph of a graph $G$, denoted by $\mathcal{R}_{\ell}(G)$, is the graph whose vertices are the proper $\ell$-colorings of $G$, with an edge between two colorings if they differ in color on exactly one vertex. For any graph $G$ of treewidth at most $2$, Bousquet and Perarnau showed that $\mathcal{R}_\ell(G)$ has linear diameter for $\ell\geq 6$. This result was later extended by Bartier, Bousquet, and Heinrich, who proved that $\mathcal{R}_5(G)$ also has linear diameter. In this paper, we show that for each $\ell\geq 5$, the $\ell$-reconfiguration graphs of $K_{2,3}$-minor-free graphs, some of which include graphs of treewidth $3$, have linear diameter. As a key step in our proof, we also establish that the $(\ell-1)$-reconfiguration graphs of cactus graphs have linear diameter.

math.CO↗

arXiv2025

Solving the fully nonlinear Monge-Ampère equation using the Legendre-Kolmogorov-Arnold Network method

In this paper, we propose a novel neural network framework, the Legendre-Kolmogorov-Arnold Network (Legendre-KAN) method, designed to solve fully nonlinear Monge-Ampère equations with Dirichlet boundary conditions. The architecture leverages the orthogonality of Legendre polynomials as basis functions, significantly enhancing both convergence speed and solution accuracy compared to traditional methods. Furthermore, the Kolmogorov-Arnold representation theorem provides a strong theoretical foundation for the interpretability and optimization of the network. We demonstrate the effectiveness of the proposed method through numerical examples, involving both smooth and singular solutions in various dimensions. This work not only addresses the challenges of solving high-dimensional and singular Monge-Ampère equations but also highlights the potential of neural network-based approaches for complex partial differential equations. Additionally, the method is applied to the optimal transport problem in image mapping, showcasing its practical utility in geometric image transformation. This approach is expected to pave the way for further enhancement of KAN-based applications and numerical solutions of PDEs across a wide range of scientific and engineering fields.

math.NA↗

arXiv2024

Arc-disjoint in- and out-branchings in semicomplete split digraphs

An \emph{out-tree (in-tree)} is an oriented tree where every vertex except one, called the \emph{root}, has in-degree (out-degree) one. An \emph{out-branching $B^+_u$ (in-branching $B^-_u$)} of a digraph $D$ is a spanning out-tree (in-tree) rooted at $u$. A \emph{good $(u,v)$-pair} in $D$ is a pair of branchings $B^+_u, B^-_v$ which are arc-disjoint. Thomassen proved that deciding whether a digraph has any good pair is NP-complete. A \emph{semicomplete split digraph} is a digraph where the vertex set is the disjoint union of two non-empty sets, $V_1$ and $V_2$, such that $V_1$ is an independent set, the subdigraph induced by $V_2$ is semicomplete, and every vertex in $V_1$ is adjacent to every vertex in $V_2$. In this paper, we prove that every $2$-arc-strong semicomplete split digraph $D$ contains a good $(u, v)$-pair for any choice of vertices $u, v$ of $D$, thereby confirming a conjecture by Bang-Jensen and Wang [Bang-Jensen and Wang, J. Graph Theory, 2024].

math.CO↗

arXiv2024

A complete characterization of split digraphs with a strong arc decomposition

A \textbf{strong arc decomposition} of a (multi-)digraph $D(V, A)$ is a partition of its arc set $A$ into two disjoint arc sets $A_1$ and $A_2$ such that both of the spanning subdigraphs $D(V, A_1)$ and $D(V, A_2)$ are strong. In this paper, we fully characterize all split digraphs that do not have a strong decomposition. This resolves two problems proposed by Bang-Jensen and Wang and contributes to a series of efforts aimed at addressing this problem for specific graph classes. This work continues the research on semicomplete composition [Bang-Jensen, Gutin and Yeo, J. Graph Theory, 2020]; on locally semicomplete digraphs [Bang-Jensen and Huang, J. Combin. Theory Ser. B, 2010]; on a type of tournaments [Bang-Jensen and Yeo, Combinatorica, 2004].

math.CO↗

arXiv2019

Limited Aperture Inverse Scattering Problems using Bayesian Approach and Extended Sampling Method

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is formulated as a statistical model using the Baye's formula. The well-posedness is proved in the sense of the Hellinger metric. The extended sampling method is modified to provide the initial guess of the target location, which is critical to the fast convergence of the MCMC algorithm. An extensive numerical study is presented to illustrate the performance of the proposed method.

math.AP↗