arXiv subjects

Zihao Song

Publications and source records attributed to Zihao Song.

At least 19 recordsLinked to original sources

arXiv2026

Fractional phase slips across the charge-density-wave domain walls in 1-T TiSe2

The microscopic origin of the charge density wave (CDW) in 1\textit{T}-TiSe$_2$ remains controversial, with competing scenarios based on phonon-driven lattice instability and electronically driven excitonic correlations. Here, we combine low-temperature scanning tunneling microscopy with two-dimensional lock-in phase analysis to directly resolve the local CDW phase in real space and track its evolution across individual domain walls. In homogeneous regions, the CDW phase remains uniform; by contrast, across domain walls we uncover a robust and reproducible $2\pi/3$ phase shift that occurs collectively in all three symmetry-related CDW components. This nontrivial and correlated phase-slip configuration places stringent constraints on the order-parameter manifold and challenges the simplest purely phonon-driven commensurate lock-in picture, which would instead predict a $\pi$ phase shift. A minimal free-energy model incorporating both electron-phonon and electron-hole interactions reproduces the observed phase behavior and indicates that electronic interactions play an important role in shaping the local phase structure of the CDW order. These results establish domain walls as direct real-space probes of the microscopic interactions underlying multicomponent order and provide a general phase-resolved framework for constraining competing ordering mechanisms in correlated materials.

cond-mat.str-el↗

arXiv2026

High Mach number limit for the 3D Euler-Poisson equations of ion dynamics

In this paper, we study the global dynamics of the 3D ionic Euler-Poisson equations with the parameter of Mach number $\varepsilon$. We first establish the global well-posedness and scattering for the high Mach number regime $0<\varepsilon\leq1$ and pressureless case $\varepsilon=0$. Moreover, we prove the high Mach number limit, showing that the profile of the solution for ionic Euler-Poisson equations converged to that of the pressureless equation as $\varepsilon\rightarrow0$. Our approach combines energy estimates, dispersive estimates and the normal form method. The major difficulty lies in establishing the uniform estimates with respect to the parameter, as the dispersive or resonance structure degenerates when $\varepsilon$ tends to 0. A crucial observation is that despite the disappearance of the pressure ($\varepsilon\rightarrow0$), dispersive phase function always remains a wave-type structure in zero frequencies, which enables us to derive linear and bilinear multiplier estimates adapted to the uniformity of Mach number parameter.

math.AP↗

arXiv2026

Model-Based and Data-Driven Hierarchical Control and Topology Co-Design for Robust Networked Systems

In this paper, we consider a class of networked systems comprising an interconnected set of linear subsystems, disturbance inputs, and performance outputs. Using dissipativity theory, we first propose a model-based hierarchical control design strategy to ensure the closed-loop networked system is dissipative from its disturbance inputs to performance outputs. This involves designing local controllers for each subsystem to enforce local dissipativity guarantees, which are then exploited to co-design distributed global controllers and the interconnection topology to enforce global dissipativity guarantees while optimizing interconnection topology costs. The overall design process requires only solving a sequence of linear matrix inequality (LMI) problems, thereby retaining compositionality and decentralizability while avoiding non-convex, iterative design processes that are inefficient and centralized. This model-based hierarchical control design strategy assumes the knowledge of the subsystem dynamics, which may not hold in many real-world networked systems. Motivated by this, we also propose a data-driven hierarchical control design strategy that assumes only the availability of rich input-state-output trajectory data from the subsystems. The proposed data-driven design process assumes that the unknown disturbances affecting the subsystem dynamics are bounded by a quadratic matrix inequality (relaxing conventional bounds) and accounts for this by using the matrix S-lemma. Finally, the effectiveness of the proposed model-based and data-driven hierarchical control designs is illustrated for a networked system representing a DC microgrid, with the aim of enforcing robust (dissipative) voltage regulation and current sharing.

eess.SY↗

arXiv2026

Dreaming when Necessary: Advancing World Action Models with Adaptive Multi-Modal Reasoning

World Action Models (WAMs) offer a promising approach to embodied intelligence, yet existing methods rely heavily on video prediction as action priors and lack adaptive multimodal reasoning, limiting their effectiveness on long-horizon, complex tasks. We observe that WAMs require different multimodal reasoning modes under different execution contexts: textual reasoning is essential during task transitions to guide high-level action prediction, while visual reasoning is critical during fine-grained manipulation for precise control. Motivated by this observation, we propose \textbf{AdaWAM}, a world action model with adaptive multimodal reasoning abilities. AdaWAM integrates a lightweight dynamic router that autonomously triggers textual or visual reasoning as needed during task execution. Experiments on both simulated and real-world embodied tasks show that AdaWAM substantially improves inference efficiency while outperforming state-of-the-art embodied policies. Codes and demos are available at: https://adawam.github.io/.

cs.RO↗

arXiv2026

Well-posedness and vanishing rotational limit for the rotating incompressible Navier-Stokes equations in hybird Besov space

We establish the well-posedness of the 3D rotating incompressible Navier-Stokes equations with critical initial data $u_{0,\Omega}\in X_{0,q,p}^{\Omega}$ for $p<5$, where $X_{0,q,p}^{\Omega}$ is defined by the norm \begin{equation*} \begin{aligned} &\|u_{0,\Omega}\|_{X_{0,q,p}^{\Omega}}:= \Omega^{3- \frac{6}{q}}\|u_{0,\Omega}\|_{\dot{B}_{q,\infty}^{-7+\frac{15}{q}}}^{\ell_\Omega} +\|u_{0,\Omega}\|_{\dot{B}_{p,\infty}^{-1+\frac{3}{p}}}^{h_\Omega}. \end{aligned} \end{equation*} This extends the previous results by Chen, Miao, and Zhang (\cite{CMZ2013}). The main ingredients are a new global-in-time dissipative-dispersive estimate for the Stokes--Coriolis semigroup and corresponding bilinear estimates. Furthermore, we establish the vanishing rotational limit for the 3D rotating Navier-Stokes equations as $\Omega\rightarrow 0^{+}$.

math.AP↗

arXiv2026

Robust Tensor Regression with Nonconvexity: Algorithmic and Statistical Theory

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression method for analyzing high-dimensional tensor data with heavy-tailed random noise. The proposed method is based on a nonconvex relaxation of the tensor tubal rank within a general optimization framework, which allows for nonconvexity in both the loss and penalty functions. We develop an implementable estimation algorithm and establish its global convergence under some mild assumptions. Furthermore, we provide general statistical theories regarding stationary point, including the rates of convergence and bounds on the prediction error. These theoretical results cover many important models, such as linear models, generalized linear models, and Huber regression, and even encompass some nonconvex losses like correntropy and minimum distance criterion-induced losses. Supportive numerical evidence is provided through simulations and application studies.

stat.ME↗

arXiv2026

From Sustainable Materials to User-Centered Sustainability: Material Experience in Art Healing

This study develops sustainable materials using hydrogel as the matrix and explores the transition from sustainable materials to user-centered sustainability, with a particular focus on achieving art healing through material experience. The findings reveal that "Aesthetic" property exert the greatest influence on art healing in the context of multimodal material experiences involving visual, tactile, and smell, followed by "Intrinsic" property, whereas "Physical" property have a comparatively limited effect. Furthermore, the study proposes a material experience framework that enables designers to systematically and holistically understanding material characteristics. It highlights the importance of considering users' psychological perceptions and emotional needs in the material design process.

cs.HC↗

arXiv2026

Electrostatic effects on critical regularity and long-time behavior of viscous compressible fluids

We consider the compressible Navier-Stokes-Poisson equations in $\mathbb{R}^d$ ($d\geq2$), a classical model for barotropic compressible flows coupled with a self-consistent electrostatic potential. We show that the electrostatic coupling has a significant impact on the long-time dynamics of solutions due to its underlying Klein-Gordon structure. As a first result, we prove the global well-posedness of the Cauchy problem with initial data near equilibrium in the full-frequency $L^{p}$-type critical Besov space \emph{without relying on hyperbolic symmetrization}. Compared with the Poisson-free case studied in several milestone works [Charve and Danchin, Arch. Rational Mech. Anal., 198 (2010), 233-271; Chen, Miao and Zhang, Commun. Pure Appl. Math., 63 (2010), 1173-1224; Haspot, Arch. Rational Mech. Anal., 202 (2011), 427-460], we remove the extra $L^{2}$ assumption in low frequencies and extend the admissible choice of $p$ to the sharp range $1\leq p<2d$. This is, to the best of our knowledge, the first result in compressible fluids that allows the initial velocity field to be highly oscillatory across all frequencies. Furthermore, stemming from the Poisson coupling, the density and velocity exhibit distinct low-frequency behaviors. Motivated by this feature, we propose a general $L^p$-type low-frequency assumption and establish the optimal convergence rates of global solutions toward equilibrium. For a broad class of indices, this assumption yields faster decay than those obtained under the classical $L^1$ framework. To this end, we develop a time-weighted energy method, which is of interest and enables us to capture maximal decay estimates without additional smallness of initial data.

math.AP↗

arXiv2026

The compressible Euler system with damping in hybrid Besov spaces: global well-posedness and relaxation limit

We investigate the global well-posedness of the compressible Euler system with damping in Rd (d\geq1) and its relaxation limit toward the porous medium equation. In [12], the first author and Danchin studied these two problems in hybrid Besov spaces, where the high-frequency components of the solution are bounded in L2-based norms, while the low-frequency components are controlled in Lp-based norms with p\in[2,\max{4,\frac{2d}{d-2}}]. Motivated by the observation that the limit system is well-posed in Lp-based spaces for p\in[2, \infty), we extend the low-frequency analysis to this full range, thereby providing a more unified framework for studying such relaxation limits. The core of our proof consists in establishing refined product and commutator estimates describing sharply the interactions between the high, medium, and low-frequency regimes. A key observation underlying our analysis is that the product of two functions localized at low frequencies generates only interactions between low and medium frequencies, never purely high-frequency ones. Consequently, for a suitable choice of frequency threshold, the high-frequency projection of the product of two functions localized low frequencies vanishes.

math.AP↗

arXiv2025

Funnel-Based Online Recovery Control for Nonlinear Systems With Unknown Dynamics

In this paper, we focus on recovery control of nonlinear systems from attacks or failures. The main challenges of this problem lie in (1) learning the unknown dynamics caused by attacks or failures with formal guarantees, and (2) finding the invariant set of states to formally ensure the state deviations allowed from the nominal trajectory. To solve this problem, we propose to apply the Recurrent Equilibrium Networks (RENs) to learn the unknown dynamics using the data from the real-time system states. The input-output property of this REN model is guaranteed by incremental integral quadratic constraints (IQCs). Then, we propose a funnel-based control method to achieve system recovery from the deviated states. In particular, a sufficient condition for nominal trajectory stabilization is derived together with the invariant funnels along the nominal trajectory. Eventually, the effectiveness of our proposed control method is illustrated by a simulation example of a DC microgrid control application.

eess.SY↗

arXiv2025

ODesign: A World Model for Biomolecular Interaction Design

Biomolecular interactions underpin almost all biological processes, and their rational design is central to programming new biological functions. Generative AI models have emerged as powerful tools for molecular design, yet most remain specialized for individual molecular types and lack fine-grained control over interaction details. Here we present ODesign, an all-atom generative world model for all-to-all biomolecular interaction design. ODesign allows scientists to specify epitopes on arbitrary targets and generate diverse classes of binding partners with fine-grained control. Across entity-, token-, and atom-level benchmarks in the protein modality, ODesign demonstrates superior controllability and performance to modality-specific baselines. Extending beyond proteins, it generalizes to nucleic acid and small-molecule design, enabling interaction types such as protein-binding RNA/DNA and RNA/DNA-binding ligands that were previously inaccessible. By unifying multimodal biomolecular interactions within a single generative framework, ODesign moves toward a general-purpose molecular world model capable of programmable design. ODesign is available at https://odesign.lglab.ac.cn ,

q-bio.BM↗

arXiv2025

Global well-posedness for the 3D compressible Navier-Stokes equations in optimal Besov space

We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space $\mathbb{X}_p=\dot{B}_{p,1}^{3/p}(\mathbb{R}^3)\times \dot{B}_{p,1}^{-1+3/p}(\mathbb{R}^3)$ for $2\leq p<6$ and $(\rho_0-1,\rho_0u_0)$ satisfies an additional low frequency condition. Our results extend the previous results in \cite{FD2010, CMZ2010, H20112} where $p<4$ is needed for high frequency, to the optimal range $p<6$. The main ingredients of the proof consist of: a novel nonlinear transform that uses momentum formulation for low-frequency and effective velocity method for high frequency, and estimate of parabolic-dispersive semigroup that enables a $L^q$-framework for low frequency.

math.AP↗

arXiv2025

Mesh Stability Guaranteed Rigid Body Networks Using Control and Topology Co-Design

Merging and splitting are of great significance for rigid body networks in making such networks reconfigurable. The main challenges lie in simultaneously ensuring the compositionality of the distributed controllers and the mesh stability of the entire network. To this end, we propose a decentralized control and topology co-design method for rigid body networks, which enables flexible joining and leaving of rigid bodies without the need to redesign the controllers for the entire network after such maneuvers. We first provide a centralized linear matrix inequality (LMI)-based control and topology co-design optimization of the rigid body networks with a formal mesh stability guarantee. Then, these centralized mesh stability constraints are made decentralized by a proposed alternative set of sufficient conditions. Using these decentralized mesh stability constraints and Sylvester's criterion-based decentralization techniques, the said centralized LMI problem is equivalently broken down into a set of smaller decentralized LMI problems that can be solved at each rigid body, enabling flexible merging/splitting of rigid bodies. Finally, the effectiveness of the proposed co-design method is illustrated based on a specifically developed simulator and a comparison study with respect to a state-of-the-art method.

eess.SY↗

arXiv2025

Graph Neural Network-Based Distributed Optimal Control for Linear Networked Systems: An Online Distributed Training Approach

In this paper, we consider the distributed optimal control problem for discrete-time linear networked systems. In particular, we are interested in learning distributed optimal controllers using graph recurrent neural networks (GRNNs). Most of the existing approaches result in centralized optimal controllers with offline training processes. However, as the increasing demand of network resilience, the optimal controllers are further expected to be distributed, and are desirable to be trained in an online distributed fashion, which are also the main contributions of our work. To solve this problem, we first propose a GRNN-based distributed optimal control method, and we cast the problem as a self-supervised learning problem. Then, the distributed online training is achieved via distributed gradient computation, and inspired by the (consensus-based) distributed optimization idea, a distributed online training optimizer is designed. Furthermore, the local closed-loop stability of the linear networked system under our proposed GRNN-based controller is provided by assuming that the nonlinear activation function of the GRNN-based controller is both local sector-bounded and slope-restricted. The effectiveness of our proposed method is illustrated by numerical simulations using a specifically developed simulator.

eess.SY↗

arXiv2024

Application of Physics-Informed Neural Networks in Removing Telescope Beam Effects

This study introduces {\tt{PI-AstroDeconv}}, a physics-informed semi-supervised learning method specifically designed for removing beam effects in astronomical telescope observation systems. The method utilizes an encoder-decoder network architecture and combines the telescope's point spread function or beam as prior information, while integrating fast Fourier transform accelerated convolution techniques into the deep learning network. This enables effective removal of beam effects from astronomical observation images. {\tt{PI-AstroDeconv}} can handle multiple PSFs or beams, tolerate imprecise measurements to some extent, and significantly improve the efficiency and accuracy of image deconvolution. Therefore, this architecture is particularly suitable for astronomical data processing that does not rely on annotated data. To validate the reliability of the architecture, we used the SKA Science Data Challenge 3a datasets and compared it with the $\tt{CLEAN}$ deconvolution method at the 21-cm power spectrum level. The results demonstrate that our algorithm not only restores details and reduces blurriness in celestial images at the pixel level but also more accurately recovers the true neutral hydrogen power spectrum at the power spectrum level.

astro-ph.IM↗

arXiv2024

Spectuner: A Framework for Automated Line Identification of Interstellar Molecules

Interstellar molecules, which play an important role in astrochemistry, are identified using observed spectral lines. Despite the advent of spectral analysis tools in the past decade, the identification of spectral lines remains a tedious task that requires extensive manual intervention, preventing us from fully exploiting the vast amounts of data generated by large facilities such as ALMA. This study aims to address the aforementioned issue by developing a framework of automated line identification. We introduce a robust spectral fitting technique applicable for spectral line identification with minimal human supervision. Our method is assessed using published data from five line surveys of hot cores, including W51, Orion-KL, Sgr B2(M), and Sgr B2(N). By comparing the identified lines, our algorithm achieves an overall recall of ~ 74% - 93%, and an average precision of ~ 78% - 92%. Our code, named Spectuner, is publicly available on GitHub.

astro-ph.GA↗

arXiv2024

Global dynamics of large solution for the compressible Navier-Stokes-Korteweg equations

In this paper, we study the Navier-Stokes-Korteweg equations governed by the evolution of compressible fluids with capillarity effects. We first investigate the global well-posedness of solution in the critical Besov space for large initial data. Contrary to pure parabolic methods in Charve, Danchin and Xu \cite{CDX}, we also take the strong dispersion due to large capillarity coefficient $\kappa$ into considerations. By establishing a dissipative-dispersive estimate, we are able to obtain uniform estimates and incompressible limits in terms of $\kappa$ simultaneously. Secondly, we establish the large time behaviors of the solution. We would make full use of both parabolic mechanics and dispersive structure which implicates our decay results without limitations for upper bound of derivatives while requiring no smallness for initial assumption.

math.AP↗

arXiv2024

Global dynamics of Kato's solutions for the 3D incompressible micropolar system

We consider the global well-posedness and decay rates for solutions of 3D incompressible micropolar equation in the critical Besov space. Spectrum analysis allows us to find not only parabolic behaviors of solutions, but also damping effect of angular velocity in the low frequencies. Based on this observation, we establish the global well-posedness with more general regularity on the initial data. The approach concerns large time behaviors is so-called the Gevrey method which bases on the parabolic mechanics of the micropolar system. This method enables us even to derive decay of \textit{arbitrary} higher order derivatives by transforming it into the control of the radius of analyticity under a particular regularity. To bound the growth of the radius of analyticity in general $L^p$ Besov spaces, we shall develop some new techniques concern Gevrey estimates, especially an extended Coifman-Meyer theory, to cover those endpoint Lebesgue framework.

math.AP↗