arXiv subjects

Zhiwen Zhao

Publications and source records attributed to Zhiwen Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Local behavior for solutions to inhomogeneous singular parabolic $p$-Laplace equations

It is known that a major difficulty in proving Hölder regularity for solutions to quasilinear singular parabolic equations of $p$-Laplace type via the method of intrinsic scaling is to establish the decay estimate of the space-time measure of level sets. In this paper, we consider an inhomogeneous singular parabolic $p$-Laplace equation with nonnegative time-independent forcing and Dirichlet data. By combining a time-rescaling argument with $L^\infty$ comparison estimates, we derive Lipschitz regularity in time after any fixed positive elapsed time, which reduces the problem to an elliptic-type decay estimate for the spatial measure of level sets that is essentially uniform in time. This reduction enables us to address the above obstacle.

math.AP↗

arXiv2026

A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes

With the advancement of deep learning technologies, various neural network-based Granger causality models have been proposed. Although these models have demonstrated notable improvements, several limitations remain. Most existing approaches adopt the component-wise architecture, necessitating the construction of a separate model for each time series, which results in substantial computational costs. In addition, imposing the sparsity-inducing penalty on the first-layer weights of the neural network to extract causal relationships weakens the model's ability to capture complex interactions. To address these limitations, we propose Gradient Regularization-based Neural Granger Causality (GRNGC), which requires only one time series prediction model and applies $L_{1}$ regularization to the gradient between model's input and output to infer Granger causality. Moreover, GRNGC is not tied to a specific time series forecasting model and can be implemented with diverse architectures such as KAN, MLP, and LSTM, offering enhanced flexibility. Numerical simulations on DREAM, Lorenz-96, fMRI BOLD, and CausalTime show that GRNGC outperforms existing baselines and significantly reduces computational overhead. Meanwhile, experiments on real-world DNA, Yeast, HeLa, and bladder urothelial carcinoma datasets further validate the model's effectiveness in reconstructing gene regulatory networks.

cs.LG↗

arXiv2026

Readout and PID using AIML for SoLID High Background Cherenkov Detectors

We present the development of readout electronics and artificial-intelligence-based particle-identification methods for the SoLID Cherenkov detectors at Jefferson Lab. To operate in the high-rate, high-background SoLID environment, we designed a MAROC sum readout system for multianode photomultiplier tubes that provides simultaneous pixel, quadrant-sum, and total-sum signals. Bench studies show that the system can sustain rates at or above those expected for SoLID while maintaining acceptable pedestal behavior and signal linearity. Using realistic Geant4 simulations for the heavy-gas Cherenkov detector, we then investigate $π/K$ separation with beam-related background. A simple photoelectron-counting cut is insufficient under these conditions, whereas multilayer perceptron models trained on PMT, quad, and pixel readout data perform substantially better. The quad and pixel readout schemes achieve pion and kaon efficiencies above 90\% and clearly outperform PMT-only readout. These results demonstrate that the combination of high-rate MAROC sum electronics and AIML-based pattern recognition provides a practical path toward robust SoLID Cherenkov PID.

physics.ins-det↗

arXiv2026

Nonuniqueness for high-dimensional ideal MHD equations via differential inclusion

In this paper, we establish the non-uniqueness of solutions to the ideal magnetohydrodynamics equations in any dimension greater than three by proving the existence of infinitely many compactly supported weak solutions. In particular, these solutions fail to conserve the total energy. Our proof relies on the differential inclusion framework tailored to the geometry of ideal MHD system, which enables the simultaneous use of Baire category method and convex integration scheme.

math.AP↗

arXiv2025

Study of SIDIS Unpolarized Cross Sections from a $^3$He Target with the Solenoidal Large Intensity Device at JLab

In this paper we present a detailed impact study of semi-inclusive deep inelastic scattering unpolarized cross sections' measurements using the proposed SoLID apparatus at Jefferson Lab. This type of data, collected at large Bjorken $x_{bj}$, moderate values of $Q^2$ and small values of the transverse momentum of produced hadrons, $P_{hT}$, allows to study transverse momentum dependent (TMD) parton distribution and fragmentation functions in a still poorly explored region. We present the projected results for charged light mesons based on simulated data. For the azimuthal-angle integrated cross sections we adopt the TMD framework up to the next-to-next-to-next-to-leading-logarithmic (N3LL) accuracy, while a simpler TMD parton model is employed for the study of azimuthal angular dependencies.

nucl-ex↗

arXiv2025

An Interpretable Multi-Plane Fusion Framework With Kolmogorov-Arnold Network Guided Attention Enhancement for Alzheimer's Disease Diagnosis

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that severely impairs cognitive function and quality of life. Timely intervention in AD relies heavily on early and precise diagnosis, which remains challenging due to the complex and subtle structural changes in the brain. Most existing deep learning methods focus only on a single plane of structural magnetic resonance imaging (sMRI) and struggle to accurately capture the complex and nonlinear relationships among pathological regions of the brain, thus limiting their ability to precisely identify atrophic features. To overcome these limitations, we propose an innovative framework, MPF-KANSC, which integrates multi-plane fusion (MPF) for combining features from the coronal, sagittal, and axial planes, and a Kolmogorov-Arnold Network-guided spatial-channel attention mechanism (KANSC) to more effectively learn and represent sMRI atrophy features. Specifically, the proposed model enables parallel feature extraction from multiple anatomical planes, thus capturing more comprehensive structural information. The KANSC attention mechanism further leverages a more flexible and accurate nonlinear function approximation technique, facilitating precise identification and localization of disease-related abnormalities. Experiments on the ADNI dataset confirm that the proposed MPF-KANSC achieves superior performance in AD diagnosis. Moreover, our findings provide new evidence of right-lateralized asymmetry in subcortical structural changes during AD progression, highlighting the model's promising interpretability.

cs.CV↗

arXiv2025

SFNet: A Spatial-Frequency Domain Deep Learning Network for Efficient Alzheimer's Disease Diagnosis

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that predominantly affects the elderly population and currently has no cure. Magnetic Resonance Imaging (MRI), as a non-invasive imaging technique, is essential for the early diagnosis of AD. MRI inherently contains both spatial and frequency information, as raw signals are acquired in the frequency domain and reconstructed into spatial images via the Fourier transform. However, most existing AD diagnostic models extract features from a single domain, limiting their capacity to fully capture the complex neuroimaging characteristics of the disease. While some studies have combined spatial and frequency information, they are mostly confined to 2D MRI, leaving the potential of dual-domain analysis in 3D MRI unexplored. To overcome this limitation, we propose Spatio-Frequency Network (SFNet), the first end-to-end deep learning framework that simultaneously leverages spatial and frequency domain information to enhance 3D MRI-based AD diagnosis. SFNet integrates an enhanced dense convolutional network to extract local spatial features and a global frequency module to capture global frequency-domain representations. Additionally, a novel multi-scale attention module is proposed to further refine spatial feature extraction. Experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that SFNet outperforms existing baselines and reduces computational overhead in classifying cognitively normal (CN) and AD, achieving an accuracy of 95.1%.

eess.IV↗

arXiv2025

A Nash-Kuiper theorem for isometric immersions in a high codimension

This paper is devoted to investigating the isometric immersion problem of Riemannian manifolds in a high codimension. It has recently been demonstrated that any short immersion from an $n$-dimensional smooth compact manifold into $2n$-dimensional Euclidean space can be uniformly approximated by $C^{1,θ}$ isometric immersions with any $θ\in(0,1/(n+2))$ in dimensions $n\geq3$. In this paper, we improve the Hölder regularity of the constructed isometric immersions in the local setting, achieving $C^{1,θ}$ for all $θ\in(0,1/n)$ in odd dimensions and all $θ\in(0,1/(n+1))$ in even dimensions. Moreover, we also establish explicit $C^{1}$ estimates for the isometric immersions, which indicate that the larger the initial metric error is, the greater the $C^{1}$ norms of the resulting isometric maps become, meaning that their slope become steeper.

math.DG↗

arXiv2025

Nonuniqueness analysis on the Navier-Stokes equation in $C_{t}L^{q}$ space

In the presence of any prescribed kinetic energy, we implement the intermittent convex integration scheme with $L^{q}$-normalized intermittent jets to give a direct proof for the existence of solution to the Navier-Stokes equation in $C_{t}L^{q}$ for some uniform $2<q\ll3$ without the help of interpolation inequality. The result shows the sharp nonuniqueness that there evolve infinite nontrivial weak solutions of the Navier-Stokes equation starting from zero initial data. Furthermore, we improve the regularity of solution to be of $C_{t}W^{α,q}$ in virtue of the fractional Gagliardo-Nirenberg inequalities with some $0<α\ll1$. More importantly, the proof framework provides a stepping stone for future progress on the method of intermittent convex integration due to the fact that $L^{q}$-normalized building blocks carry the threshold effect of the exponent $q$ arbitrarily close to the critical value $3$.

math.AP↗

arXiv2025

Kolmogorov-Arnold Networks for Time Series Granger Causality Inference

We propose the Granger causality inference Kolmogorov-Arnold Networks (KANGCI), a novel architecture that extends the recently proposed Kolmogorov-Arnold Networks (KAN) to the domain of causal inference. By extracting base weights from KAN layers and incorporating the sparsity-inducing penalty and ridge regularization, KANGCI effectively infers the Granger causality from time series. Additionally, we propose an algorithm based on time-reversed Granger causality that automatically selects causal relationships with better inference performance from the original or time-reversed time series or integrates the results to mitigate spurious connectivities. Comprehensive experiments conducted on Lorenz-96, Gene regulatory networks, fMRI BOLD signals, VAR, and real-world EEG datasets demonstrate that the proposed model achieves competitive performance to state-of-the-art methods in inferring Granger causality from nonlinear, high-dimensional, and limited-sample time series.

cs.LG↗

arXiv2024

On a class of anisotropic Muckenhoupt weights and their applications to $p$-Laplace equations

In this paper, a class of anisotropic weights having the form of $|x'|^{θ_{1}}|x|^{θ_{2}}|x_{n}|^{θ_{3}}$ in dimensions $n\geq2$ is considered, where $x=(x',x_{n})$ and $x'=(x_{1},...,x_{n-1})$. We first find the optimal range of $(θ_{1},θ_{2},θ_{3})$ such that this type of weights belongs to the Muckenhoupt class $A_{p}$. Then we further study its doubling property, which shows that it provides an example of a doubling measure but is not in $A_{p}$. As a consequence, we obtain anisotropic weighted Poincaré and Sobolev inequalities, which are used to study the local behavior for solutions to non-homogeneous weighted $p$-Laplace equations.

math.AP↗

arXiv2024

Local regularity for solutions to quasi-linear singular parabolic equations with anisotropic weights

This paper develops a concise procedure for the study on local behavior of solutions to anisotropically weighted quasi-linear singular parabolic equations of $p$-Laplacian type, which is realized by improving the energy inequalities and applying intrinsic scaling factor to the De Giorgi truncation method. In particular, it also presents a new proof for local Hölder continuity of the solution in the unweighted case.

math.AP↗

arXiv2023

Local behavior for solutions to anisotropic weighted quasilinear degenerate parabolic equations

This paper aims to study the local behavior of solutions to a class of anisotropic weighted quasilinear degenerate parabolic equations with the weights comprising two power-type weights of different dimensions. We first capture the asymptotic behavior of the solution near the singular or degenerate point of the weights. In particular, we find an explicit upper bound on the decay rate exponent determined by the structures of the equations and weights, which can be achieved under certain condition and meanwhile reflects the damage effect of the weights on the regularity of the solution. Furthermore, we prove the local Hölder regularity of solutions to non-homogeneous parabolic $p$-Laplace equations with single power-type weights.

math.AP↗

arXiv2023

Regularity and stability for solutions to elliptic equations and systems arising from high-contrast composites

The main objective of this paper is to study the regularity and stability for solutions to the conductivity problems with degenerate coefficients in the presence of two rigid conductors, as one conductor keeps motionless and another conductor moves in some direction by a sufficiently small translational distance. We will show that the solutions are smooth and stable with respect to the small translational distance. Our results contain the following three cases: two perfect conductors, two insulators, a perfect conductor and an insulator. Further, we extend the results to the elasticity problem modeled by the Lamé system with partially infinite coefficients.

math.AP↗

arXiv2023

Stress concentration for nonlinear insulated conductivity problem with adjacent inclusions

A high-contrast two-phase nonlinear composite material with adjacent inclusions of $m$-convex shapes is considered for $m>2$. The mathematical formulation consists of the insulated conductivity problem with $p$-Laplace operator in $\mathbb{R}^{d}$ for $p>1$ and $d\geq2$. The stress, which is the gradient of the solution, always blows up with respect to the distance $\varepsilon$ between two inclusions as $\varepsilon$ goes to zero. We first establish the pointwise upper bound on the gradient possessing the singularity of order $\varepsilon^{-β}$ with $β=(1-α)/m$ for some $α\geq0$, where $α=0$ if $d=2$ and $α>0$ if $d\geq3$. In particular, we give a quantitative description for the range of horizontal length of the narrow channel in the process of establishing the gradient estimates, which provides a clear understanding for the applied techniques and methods. For $d\geq2$, we further construct a supersolution to sharpen the upper bound with any $β>(d+m-2)/(m(p-1))$ when $p>d+m-1$. Finally, a subsolution is also constructed to show the almost optimality of the blow-up rate $\varepsilon^{-1/\max\{p-1,m\}}$ in the presence of curvilinear squares. This fact reveals a novel dichotomy phenomena that the singularity of the gradient is uniquely determined by one of the convexity parameter $m$ and the nonlinear exponent $p$ except for the critical case of $p=m+1$ in two dimensions.

math.AP↗

arXiv2023

Asymptotic stability of homogeneous solutions to Navier-Stokes equations under $L^{p}$-perturbations

It is known that there has been classified for all $(-1)$-homogeneous axisymmetric no-swirl solutions of the three-dimensional Navier-Stokes equations with a possible singular ray. The main purpose of this paper is to show that the least singular solutions among such solutions other than Landau solutions to the Navier-Stokes equations are asymptotically stable under $L^{3}$-perturbations. Moreover, we establish the $L^{q}$ decay estimate with an explicit decay rate and a sharp constant for any $q>3$. For that purpose, we first study the global well-posedness of solutions to the perturbed equations under small initial data in $L_σ^{3}$ space and the local well-posedness with any initial data in $L_σ^{p}$ spaces for $p\geq3$.

math.AP↗

arXiv2023

SIDIS-RC EvGen: a Monte-Carlo event generator of semi-inclusive deep inelastic scattering with the lowest-order QED radiative corrections

SIDIS-RC EvGen is a C++ standalone Monte-Carlo event generator for studies of semi-inclusive deep inelastic scattering (SIDIS) processes at medium to high lepton beam energies. In particular, the generator contains binary and library components for generating SIDS events and calculating cross sections for unpolarized or longitudinally polarized beam and unpolarized, longitudinally or transversely polarized target. The structure of the generator incorporates transverse momentum-dependent parton distribution and fragmentation functions, whereby we obtain multi-dimensional binned simulation results, which will facilitate the extraction of important information about the three-dimensional nucleon structure from SIDIS measurements. In order to build this software, we have used recent elaborate QED calculations of the lowest-order radiative effects, applied to the leading order Born cross section in SIDIS. In this paper, we provide details on the theoretical formalism as well as the construction and operation of SIDIS-RC EvGen, e.g., how we handle the event generation process and perform multi-dimensional integration. We also provide example programs, flowcharts, and numerical results on azimuthal transverse single-spin asymmetries.

hep-ph↗

arXiv2023

The Solenoidal Large Intensity Device (SoLID) for JLab 12 GeV

The Solenoidal Large Intensity Device (SoLID) is a new experimental apparatus planned for Hall A at the Thomas Jefferson National Accelerator Facility (JLab). SoLID will combine large angular and momentum acceptance with the capability to handle very high data rates at high luminosity. With a slate of approved high-impact physics experiments, SoLID will push JLab to a new limit at the QCD intensity frontier that will exploit the full potential of its 12 GeV electron beam. In this paper, we present an overview of the rich physics program that can be realized with SoLID, which encompasses the tomography of the nucleon in 3-D momentum space from Semi-Inclusive Deep Inelastic Scattering (SIDIS), expanding the phase space in the search for new physics and novel hadronic effects in parity-violating DIS (PVDIS), a precision measurement of $J/ψ$ production at threshold that probes the gluon field and its contribution to the proton mass, tomography of the nucleon in combined coordinate and momentum space with deep exclusive reactions, and more. To meet the challenging requirements, the design of SoLID described here takes full advantage of recent progress in detector, data acquisition and computing technologies. In addition, we outline potential experiments beyond the currently approved program and discuss the physics that could be explored should upgrades of CEBAF become a reality in the future.

nucl-ex↗