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Zhehui Wang

Publications and source records attributed to Zhehui Wang.

At least 19 recordsLinked to original sources
arXiv2026

A sharp lower bound for the nodal volume of harmonic functions

Let $u$ be a non-zero real-valued harmonic function in $B_4\subset\mathbb{R}^n$ with $n\geq3$ and $u(0)=0$. We prove that $$\mathcal{H}^{n-1}\bigl(\{u(x)=0\}\cap B_2\bigr)\ge C_n\mathcal{N},$$ where $C_n$ is a positive constant depending only on $n$, and $\mathcal{N}$ is the doubling index defined by $$\mathcal{N}=\log_2\frac{\sup_{B_1}|u|}{\sup_{B_{\frac{1}{2}}}|u|}.$$ The linear dependence on $\mathcal{N}$ is optimal. This estimate confirms a folklore conjecture on the nodal volume of harmonic functions.

math.AP↗
arXiv2026

A Cheng-Yau type estimate for positive biharmonic functions

We establish a Cheng-Yau type estimate for positive biharmonic functions on complete Riemannian manifolds with Ricci curvature satisfies $Ric_g \ge -(n-1)K g$. If $u$ is a positive biharmonic function in $B_{2R}(p)$, then $$ -\frac{\Delta_g u}{u} +\frac{1}{8n}\frac{|\nabla u|_g^2}{u^2} \le C_n\left(R^{-2}+K\right) \quad\text{on }B_R(p). $$ Further, if the Ricci curvature is nonnegative, every global positive biharmonic function satisfies $\Delta_g u\equiv c$ and the sharp estimate $|\nabla u|_g^2\le2cu$ for some nonnegative constant $c$. We also show that every positive $k$-polyharmonic function has nonnegative constant $(k-1)$-st Laplacian and growth of order at most $2k-2$.

math.DG↗
arXiv2026

Quadratic Scalar Curvature Decay and Uniform Positivity in Dimensions Four through Seven

Let $4\le n\le7$ and let $(M^n,g)$ be a complete, connected, orientable, noncompact Riemannian manifold of positive scalar curvature. We prove that if the asymptotic quadratic scalar curvature coefficient of $g$ is greater than $(n-1)/n$, then $M$ carries a complete smooth metric whose scalar curvature is at least one. The threshold $(n-1)/n$ and the strict inequality are optimal. This confirms the second part of Gromov's critical rate of decay conjecture in dimensions four through seven.

math.DG↗
arXiv2026

On the proof of Bray's conjecture

Let $(M^n,g)$ be a connected, closed, smooth Riemannian manifold with dimension $n\geq 3$. There exists a positive constant $\varepsilon_n<1$ such that, if Ricci curvature $\operatorname{Ric}_g\geq \varepsilon_n(n-1)g$ and the scalar curvature $R_g\geq n(n-1)$, then the volume $V_g(M^n)$ is less than or equal to the volume of standard $n$-sphere. This confirms a conjecture by Bray in 1997.

math.DG↗
arXiv2026

Bonnet-Myers type theorems for $Q$-curvature on four-manifolds

Let $(M^4,g)$ be a complete four-dimensional Riemannian manifold. First, if the $Q$-curvature $Q_g\geq 6k^2$ and scalar curvature $R_g\geq -12k$ for some positive constant $k$, then $(M^4,g)$ is either Einstein with $Ric_g=-3kg$ or compact with $R_g\ge 12k$. As a corollary, the fundamental group $\pi_1(M^4)$ satisfies $|\pi_1(M^4)|\leq 16\pi^2/(\int_{M^4}Q_g d\mu_g),$ under the additional assumption $R_g>-12k$. Second, if the scalar curvature $R_g>0$ and $Q_g\geq \theta R_g$ for a positive constant $\theta$, then $M^4$ is compact and the diameter of $(M^4,g)$ is at most $4\pi/\sqrt{15\theta}$.

math.DG↗
arXiv2026

Fast and bright scintillators for ultrafast materials dynamics using 4th generation synchrotron

We present recent advances in fast and bright scintillators for ultrafast X-ray phase contrast imaging of dynamic materials experiments at the upgraded Advanced Photon Source (APS-U), a fourth generation synchrotron. APS-U enables hard X-ray imaging at frame rates of at least 13 MHz (corresponding to 77 ns or shorter interframe intervals), creating a new need for scintillators with faster response and higher light output than lutetium yttrium oxyorthosilicate (LYSO). For indirect imaging and diffraction with ultrafast cameras, commercial lanthanum bromide (LaBr3) and cerium bromide (CeBr3) are promising candidates. These materials exhibit decay times approximately a factor of two shorter than LYSO (around 40 ns) and lutetium oxyorthosilicate (LSO), while maintaining comparable light yield per incident X-ray photon. However, their implementation at APS-U requires addressing several challenges, including material limitations due to hygroscopicity, efficient optical coupling to imaging systems, and high quantum efficiency for conversion of scintillation light, predominantly at wavelengths below 400 nm, into detectable electronic signals. We report results from material characterization, detector integration and packaging, and beamline experiments of materials with impact. In addition, emerging scintillator classes, including perovskites and high-entropy materials, are discussed as potential alternatives for next-generation ultrafast X-ray diagnostics.

physics.ins-det↗
arXiv2026

PiMiX 2.0: AI-enhanced Data Fusion for Radiographic Imaging and Tomography

Extending earlier work in Physics-informed Meta-instrument for eXperiments (PiMiX) [1], PiMiX~2.0 is an artificial-intelligence (AI)-enhanced data-fusion and analysis framework that integrates multi-experiment multi-modal radiographic imaging and tomography (RadIT) with physics-informed reasoning and agentic AI workflows. The framework supports automated data ingestion, multimodal image processing from one or more experiments, three-dimensional (3D) and time-resolved three-dimensional (4D) reconstruction, and physics-aware interpretation of experimental observations. The PiMiX agents are designed for deployment on desktop and laptop systems commonly used in experimental workflows, while remaining scalable to high-performance computing environments for computationally intensive tasks. By coupling RadIT instrumentation and measurements with geometry, physics, computation, and statistical inference, PiMiX 2.0 aims to accelerate RadIT data processing, knowledge extraction, improve reproducibility, and enable more integrated analysis and workflows in high-temperature plasmas, nuclear fusion, advanced manufacturing, other static and dynamic experiments.

physics.ins-det↗
arXiv2026

DustNET: enabling machine learning and AI models of dusty plasmas

Dusty plasmas are ubiquitous throughout the universe, spanning laboratory and industrial plasmas, fusion devices, planetary environments, cometary comae, and interstellar media. Despite decades of research, many aspects of their behavior remain poorly understood within a unified framework. While numerous theoretical and numerical models describe specific phenomena, such as dust charging, transport, waves, and self-organization, fully predictive models across the wide range of spatial and temporal scales in both laboratory and natural systems remain elusive. Conventional plasma descriptions rely on coupled differential equations for particle densities, momenta, and energies, but their solutions are often limited by computational cost, numerical uncertainties, and incomplete knowledge of boundary conditions and transport processes. Recent advances in machine learning (ML), particularly deep neural networks, offer new opportunities to complement traditional physics-based modeling. Here we review ML and artificial intelligence (AI) approaches, termed bottom-up data-driven methods, for dusty plasma research. Central to this effort is Dust Neural nEtworks Technology (DustNET), a community-driven dataset initiative inspired by ImageNet, integrating experimental, simulation, and synthetic data to enable predictive modeling, uncertainty quantification, and multi-scale analysis. DustNET-trained models may also be deployed in real-time experimental settings under edge computing constraints. Combined with emerging multi-modal AI foundation models and autonomous agents, this framework provides a pathway toward a unified, physics-informed understanding of dusty plasmas across laboratory, industrial, space, and astrophysical environments.

physics.plasm-ph↗
arXiv2025

Solutions of the singular Yamabe problem near singular boundaries

In this paper, we investigate the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive optimal estimates, where the background metrics are not assumed to be conformally flat. Specifically, we demonstrate that for a wide class of Lipschitz domains with asymptotic conical structure, the local positive solutions are well approximated by the positive solutions in the tangent cones at singular boundary points. This extends the results of [10, 12, 26].

math.AP↗
arXiv2025

A Machine Learning-Driven Solution for Denoising Inertial Confinement Fusion Images

Neutron imaging is essential for diagnosing and optimizing inertial confinement fusion implosions at the National Ignition Facility. Due to the required 10-micrometer resolution, however, neutron image require image reconstruction using iterative algorithms. For low-yield sources, the images may be degraded by various types of noise. Gaussian and Poisson noise often coexist within one image, obscuring fine details and blurring the edges where the source information is encoded. Traditional denoising techniques, such as filtering and thresholding, can inadvertently alter critical features or reshape the noise statistics, potentially impacting the ultimate fidelity of the iterative image reconstruction pipeline. However, recent advances in synthetic data production and machine learning have opened new opportunities to address these challenges. In this study, we present an unsupervised autoencoder with a Cohen-Daubechies- Feauveau (CDF 97) wavelet transform in the latent space, designed to suppress for mixed Gaussian-Poisson noise while preserving essential image features. The network successfully denoises neutron imaging data. Benchmarking against both simulated and experimental NIF datasets demonstrates that our approach achieves lower reconstruction error and superior edge preservation compared to conventional filtering methods such as Block-matching and 3D filtering (BM3D). By validating the effectiveness of unsupervised learning for denoising neutron images, this study establishes a critical first step towards fully AI-driven, end-to-end reconstruction frameworks for ICF diagnostics.

cs.CV↗
arXiv2025

Is Quantum Optimization Ready? An Effort Towards Neural Network Compression using Adiabatic Quantum Computing

Quantum optimization is the most mature quantum computing technology to date, providing a promising approach towards efficiently solving complex combinatorial problems. Methods such as adiabatic quantum computing (AQC) have been employed in recent years on important optimization problems across various domains. In deep learning, deep neural networks (DNN) have reached immense sizes to support new predictive capabilities. Optimization of large-scale models is critical for sustainable deployment, but becomes increasingly challenging with ever-growing model sizes and complexity. While quantum optimization is suitable for solving complex problems, its application to DNN optimization is not straightforward, requiring thorough reformulation for compatibility with commercially available quantum devices. In this work, we explore the potential of adopting AQC for fine-grained pruning-quantization of convolutional neural networks. We rework established heuristics to formulate model compression as a quadratic unconstrained binary optimization (QUBO) problem, and assess the solution space offered by commercial quantum annealing devices. Through our exploratory efforts of reformulation, we demonstrate that AQC can achieve effective compression of practical DNN models. Experiments demonstrate that adiabatic quantum computing (AQC) not only outperforms classical algorithms like genetic algorithms and reinforcement learning in terms of time efficiency but also excels at identifying global optima.

quant-ph↗
arXiv2025

Coflex: Enhancing HW-NAS with Sparse Gaussian Processes for Efficient and Scalable DNN Accelerator Design

Hardware-Aware Neural Architecture Search (HW-NAS) is an efficient approach to automatically co-optimizing neural network performance and hardware energy efficiency, making it particularly useful for the development of Deep Neural Network accelerators on the edge. However, the extensive search space and high computational cost pose significant challenges to its practical adoption. To address these limitations, we propose Coflex, a novel HW-NAS framework that integrates the Sparse Gaussian Process (SGP) with multi-objective Bayesian optimization. By leveraging sparse inducing points, Coflex reduces the GP kernel complexity from cubic to near-linear with respect to the number of training samples, without compromising optimization performance. This enables scalable approximation of large-scale search space, substantially decreasing computational overhead while preserving high predictive accuracy. We evaluate the efficacy of Coflex across various benchmarks, focusing on accelerator-specific architecture. Our experimental results show that Coflex outperforms state-of-the-art methods in terms of network accuracy and Energy-Delay-Product, while achieving a computational speed-up ranging from 1.9x to 9.5x.

cs.LG↗
arXiv2025

RBFleX-NAS: Training-Free Neural Architecture Search Using Radial Basis Function Kernel and Hyperparameter Detection

Neural Architecture Search (NAS) is an automated technique to design optimal neural network architectures for a specific workload. Conventionally, evaluating candidate networks in NAS involves extensive training, which requires significant time and computational resources. To address this, training-free NAS has been proposed to expedite network evaluation with minimal search time. However, state-of-the-art training-free NAS algorithms struggle to precisely distinguish well-performing networks from poorly-performing networks, resulting in inaccurate performance predictions and consequently sub-optimal top-1 network accuracy. Moreover, they are less effective in activation function exploration. To tackle the challenges, this paper proposes RBFleX-NAS, a novel training-free NAS framework that accounts for both activation outputs and input features of the last layer with a Radial Basis Function (RBF) kernel. We also present a detection algorithm to identify optimal hyperparameters using the obtained activation outputs and input feature maps. We verify the efficacy of RBFleX-NAS over a variety of NAS benchmarks. RBFleX-NAS significantly outperforms state-of-the-art training-free NAS methods in terms of top-1 accuracy, achieving this with short search time in NAS-Bench-201 and NAS-Bench-SSS. In addition, it demonstrates higher Kendall correlation compared to layer-based training-free NAS algorithms. Furthermore, we propose NAFBee, a new activation design space that extends the activation type to encompass various commonly used functions. In this extended design space, RBFleX-NAS demonstrates its superiority by accurately identifying the best-performing network during activation function search, providing a significant advantage over other NAS algorithms.

cs.LG↗
arXiv2024

Enabling Energy-Efficient Deployment of Large Language Models on Memristor Crossbar: A Synergy of Large and Small

Large language models (LLMs) have garnered substantial attention due to their promising applications in diverse domains. Nevertheless, the increasing size of LLMs comes with a significant surge in the computational requirements for training and deployment. Memristor crossbars have emerged as a promising solution, which demonstrated a small footprint and remarkably high energy efficiency in computer vision (CV) models. Memristors possess higher density compared to conventional memory technologies, making them highly suitable for effectively managing the extreme model size associated with LLMs. However, deploying LLMs on memristor crossbars faces three major challenges. Firstly, the size of LLMs increases rapidly, already surpassing the capabilities of state-of-the-art memristor chips. Secondly, LLMs often incorporate multi-head attention blocks, which involve non-weight stationary multiplications that traditional memristor crossbars cannot support. Third, while memristor crossbars excel at performing linear operations, they are not capable of executing complex nonlinear operations in LLM such as softmax and layer normalization. To address these challenges, we present a novel architecture for the memristor crossbar that enables the deployment of state-of-the-art LLM on a single chip or package, eliminating the energy and time inefficiencies associated with off-chip communication. Our testing on BERT_Large showed negligible accuracy loss. Compared to traditional memristor crossbars, our architecture achieves enhancements of up to 39X in area overhead and 18X in energy consumption. Compared to modern TPU/GPU systems, our architecture demonstrates at least a 68X reduction in the area-delay product and a significant 69% energy consumption reduction.

cs.AI↗
arXiv2024

Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation

We investigate the Dirichlet problem of the two dimensional Lagrangian mean curvature equation in a bounded domain. Infinitely many $C^{1, \alpha} (\alpha\in (0,\frac{1}{5}))$ very weak solutions are built through Nash-Kuiper construction. Moreover, we note there are infinitely many $C^{1, \alpha}$ very weak solutions that can not be improved to be $C^{2, \alpha}$.

math.AP↗
arXiv2024

Physics-informed Meta-instrument for eXperiments (PiMiX) with applications to fusion energy

Data-driven methods (DDMs), such as deep neural networks, offer a generic approach to integrated data analysis (IDA), integrated diagnostic-to-control (IDC) workflows through data fusion (DF), which includes multi-instrument data fusion (MIDF), multi-experiment data fusion (MXDF), and simulation-experiment data fusion (SXDF). These features make DDMs attractive to nuclear fusion energy and power plant applications, leveraging accelerated workflows through machine learning and artificial intelligence. Here we describe Physics-informed Meta-instrument for eXperiments (PiMiX) that integrates X-ray (including high-energy photons such as $γ$-rays from nuclear fusion), neutron and others (such as proton radiography) measurements for nuclear fusion. PiMiX solves multi-domain high-dimensional optimization problems and integrates multi-modal measurements with multiphysics modeling through neural networks. Super-resolution for neutron detection and energy resolved X-ray detection have been demonstrated. Multi-modal measurements through MIDF can extract more information than individual or uni-modal measurements alone. Further optimization schemes through DF are possible towards empirical fusion scaling laws discovery and new fusion reactor designs.

physics.data-an↗
arXiv2023

Efficient Spiking Neural Networks with Radix Encoding

Spiking neural networks (SNNs) have advantages in latency and energy efficiency over traditional artificial neural networks (ANNs) due to its event-driven computation mechanism and replacement of energy-consuming weight multiplications with additions. However, in order to reach accuracy of its ANN counterpart, it usually requires long spike trains to ensure the accuracy. Traditionally, a spike train needs around one thousand time steps to approach similar accuracy as its ANN counterpart. This offsets the computation efficiency brought by SNNs because longer spike trains mean a larger number of operations and longer latency. In this paper, we propose a radix encoded SNN with ultra-short spike trains. In the new model, the spike train takes less than ten time steps. Experiments show that our method demonstrates 25X speedup and 1.1% increment on accuracy, compared with the state-of-the-art work on VGG-16 network architecture and CIFAR-10 dataset.

cs.NE↗