arXiv subjects

Wei Cai

Publications and source records attributed to Wei Cai.

At least 37 records · Page 2Linked to original sources

arXiv2026

Accelerated Markov Chain Monte Carlo Simulation via Neural Network-Driven Importance Sampling

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This bottleneck often stems from complex energy landscapes where the systems stay trapped in metastable states for long periods of time. Yet, the long-term evolution is controlled by the transitions between the metastable states, which are rare events and difficult to observe. We present an importance sampling method designed to accelerate the time scale of Markov chain Monte Carlo (MCMC) simulations. By employing a bias potential, our approach enhances the sampling of rare transition events while preserving the relative probabilities of distinct transition pathways. The bias potential is represented by a neural network which enables the flexibility needed for high-dimensional systems. We propose a rigorous formulation to obtain the original transition rates between metastable states using transition paths obtained from the biased simulation. We further use a branching random walk (BRW) technique to enhance efficiency and to reduce variance. The proposed methodology is validated on 2-dimensional and 14-dimensional systems, demonstrating its accuracy and scalability.

physics.comp-ph↗

arXiv2026

Link Statistics of Dislocation Network during Strain Hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

cond-mat.mtrl-sci↗

arXiv2026

Visual Attention Reasoning via Hierarchical Search and Self-Verification

Multimodal Large Language Models (MLLMs) frequently hallucinate due to their reliance on fragile, linear reasoning and weak visual grounding. We propose Visual Attention Reasoning (VAR), a reinforcement learning framework that reformulates reasoning as a hierarchical search with self-verification. VAR enforces traceable evidence grounding by generating explicit bounding boxes, guided by a novel reward function combining geometric precision and semantic sufficiency. Furthermore, it replaces linear Chain-of-Thought with a tree-search policy capable of backtracking to correct logical errors. Theoretical analysis validates the framework's reliability, and extensive experiments demonstrate that VAR significantly outperforms state-of-the-art methods on complex hallucination and safety benchmarks.

cs.AI↗

arXiv2026

Deep Neural networks for solving high-dimensional parabolic partial differential equations

The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years, deep neural networks have emerged as a promising mesh free alternative, enabling the approximation of PDE solutions in tens to thousands of dimensions. This review provides a tutorial--oriented introduction to neural--network--based methods for solving high dimensional parabolic PDEs, emphasizing conceptual clarity and methodological connections. We organize the literature around three unifying paradigms: (i) PDE residual--based approaches, including physicsinformed neural networks and their high dimensional variants; (ii) stochastic methods derived from Feynman--Kac and backward stochastic differential equation formulations; and (iii) hybrid derivative--free random difference approaches designed to alleviate the computational cost of derivatives in high dimensions. For each paradigm, we outline the underlying mathematical formulation, algorithmic implementation, and practical strengths and limitations. Representative benchmark problems--including Hamilton--Jacobi--Bellman and Black--Scholes equations in up to 1000 dimensions --illustrate the scalability, effectiveness, and accuracy of the methods. The paper concludes with a discussion of open challenges and future directions for reliable and scalable solvers of high dimensional PDEs.

math.NA↗

arXiv2026

Deep random difference method for high-dimensional quasilinear parabolic partial differential equations

Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian matrices in the PDE. In this work, we propose a deep random difference method (DRDM) that addresses these issues by approximating the convection-diffusion operator using only first-order differences and the solution by deep neural networks, thus avoiding Hessian and other derivative computations. The DRDM is implemented within a Galerkin framework to reduce sampling variance, and the solution space is explored using stochastic differential equations (SDEs) to capture the dynamics of the convection-diffusion operator. The approach is then extended to solve Hamilton-Jacobi-Bellman (HJB) equations, which recovers existing martingale deep learning methods for PDEs [{\it SIAM J. Sci. Comput.}, 47 (2025), pp. C795-C819], without using stochastic calculus. The proposed method offers two main advantages: it avoids the need to compute derivatives in PDEs and enables parallel computation of the loss function in both time and space. Moreover, a rigorous error estimate is proven for the quasi-linear parabolic equation, showing first-order accuracy in $h$, the time step used in the discretization of the SDE paths by the Euler-Maruyama scheme. Numerical experiments demonstrate that the method can efficiently and accurately solve quasilinear parabolic PDEs and HJB equations in dimensions up to $10^5$ and $10^4$, respectively.

math.NA↗

arXiv2026

On the First Passage Times of Branching Random Walks in $\mathbb R^d$

We study the first passage times of discrete-time branching random walks in ${\mathbb R}^d$ where $d\geq 1$. Here, the genealogy of the particles follows a supercritical Galton-Watson process. We provide asymptotics of the first passage times to a ball of radius one with a distance $x$ from the origin, conditioned upon survival. We provide explicitly the linear dominating term and the logarithmic correction term as a function of $x$. The asymptotics are precise up to an order of $o_{\mathbb P}(\log x)$ for general jump distributions and up to $O_{\mathbb P}(\log\log x)$ for spherically symmetric jumps. A crucial ingredient of both results is the tightness of first passage times. We also discuss an extension of the first passage time analysis to a modified branching random walk model that has been proven to successfully capture shortest path statistics in polymer networks.

math.PR↗

arXiv2025

Aetheria: A multimodal interpretable content safety framework based on multi-agent debate and collaboration

The exponential growth of digital content presents significant challenges for content safety. Current moderation systems, often based on single models or fixed pipelines, exhibit limitations in identifying implicit risks and providing interpretable judgment processes. To address these issues, we propose Aetheria, a multimodal interpretable content safety framework based on multi-agent debate and collaboration.Employing a collaborative architecture of five core agents, Aetheria conducts in-depth analysis and adjudication of multimodal content through a dynamic, mutually persuasive debate mechanism, which is grounded by RAG-based knowledge retrieval.Comprehensive experiments on our proposed benchmark (AIR-Bench) validate that Aetheria not only generates detailed and traceable audit reports but also demonstrates significant advantages over baselines in overall content safety accuracy, especially in the identification of implicit risks. This framework establishes a transparent and interpretable paradigm, significantly advancing the field of trustworthy AI content moderation.

cs.AI↗

arXiv2025

TeleAI-Safety: A comprehensive LLM jailbreaking benchmark towards attacks, defenses, and evaluations

While the deployment of large language models (LLMs) in high-value industries continues to expand, the systematic assessment of their safety against jailbreak and prompt-based attacks remains insufficient. Existing safety evaluation benchmarks and frameworks are often limited by an imbalanced integration of core components (attack, defense, and evaluation methods) and an isolation between flexible evaluation frameworks and standardized benchmarking capabilities. These limitations hinder reliable cross-study comparisons and create unnecessary overhead for comprehensive risk assessment. To address these gaps, we present TeleAI-Safety, a modular and reproducible framework coupled with a systematic benchmark for rigorous LLM safety evaluation. Our framework integrates a broad collection of 19 attack methods (including one self-developed method), 29 defense methods, and 19 evaluation methods (including one self-developed method). With a curated attack corpus of 342 samples spanning 12 distinct risk categories, the TeleAI-Safety benchmark conducts extensive evaluations across 14 target models. The results reveal systematic vulnerabilities and model-specific failure cases, highlighting critical trade-offs between safety and utility, and identifying potential defense patterns for future optimization. In practical scenarios, TeleAI-Safety can be flexibly adjusted with customized attack, defense, and evaluation combinations to meet specific demands. We release our complete code and evaluation results to facilitate reproducible research and establish unified safety baselines.

cs.CR↗

arXiv2025

Fast boundary integral method for acoustic wave scattering in two-dimensional layered media

In this paper, we present a fast boundary integral method accelerated by the fast multipole method (FMM) for acoustic wave scattering governed by the scalar Helmholtz equation in multi-layered two-dimensional media. Multiple scatterers are randomly distributed in the multi-layered medium with some scatterers possibly intersecting layer interfaces. The boundary integral formulation employs a layered-medium Green's function to enforce transmission conditions across interfaces, thus avoiding unknowns on the interfaces and significantly reducing the size of the discretized problem compared to approaches that use a free-space Green's function. To demonstrate the FMM speedup, a low-order Nyström method is used to discretize the boundary integral equation and then the resulting dense linear system is solved by GMRES iterative solver accelerated by an improved layered media FMM and a overlapping domain decomposition preconditioning. In the low frequency regime, the proposed algorithm achieves an $\mathcal O(N)$ complexity. Numerical results validate the accuracy, efficiency and robustness of the method under complex settings and various incident angles. The proposed framework provides a scalable and efficient solver for acoustic wave scattering in layered media.

math.NA↗

arXiv2025

Lithium Niobate Vertical Cavity Electro-Optic Modulator

Electro-optic modulators (EOMs) are vital for optical imaging and information processing, with free-space devices enabling LiDAR and beam control. Lithium niobate (LN), powered by the strong Pockels effect and scalable LN-on-insulator (LNOI) platform, has become a leading material for high-performance EOMs. Here we realize a vertical-cavity EOM in which an LN membrane is sandwiched between two photonic crystal (PhC) mirrors with integrated electrodes. The cavity supports sharp defect-mode resonances that shift efficiently under the Pockels effect, enabling strong modulation of transmission. Experiments show a depth of 43 % at 50 V and a bandwidth of 5 MHz. This architecture combines free-space compatibility with fabrication simplicity, opening new routes to compact electro-optic platforms for ranging, holography, and beam steering.

physics.optics↗

arXiv2025

Learning Neural Pushforward Samplers for Distributions from Fokker-Planck Equations by Weak Adversarial Training

This paper presents a new method for solving Fokker-Planck equations (FPE) by learning a neural sampler for the distribution given by the FPE via an adversarial training based on a weak formulation of the FPE where the adjoint operator of FPE acts on the test function. Such a weak formulation transforms the PDE solution problem into a Monte Carlo importance sampling problem where the FPE solution-distribution is learned through a neural pushforward map, avoiding some of the limitations of direct PDE based methods. Moreover, by using simple plane-wave test functions, derivatives on the test functions can be explicitly computed. This approach produces a natural importance sampling strategy for the FPE solution distribution with probability conservation, from which the FPE solution can be easily constructed.

math.NA↗

arXiv2025

When Safe Unimodal Inputs Collide: Optimizing Reasoning Chains for Cross-Modal Safety in Multimodal Large Language Models

Multimodal Large Language Models (MLLMs) are susceptible to the implicit reasoning risk, wherein innocuous unimodal inputs synergistically assemble into risky multimodal data that produce harmful outputs. We attribute this vulnerability to the difficulty of MLLMs maintaining safety alignment through long-chain reasoning. To address this issue, we introduce Safe-Semantics-but-Unsafe-Interpretation (SSUI), the first dataset featuring interpretable reasoning paths tailored for such a cross-modal challenge. A novel training framework, Safety-aware Reasoning Path Optimization (SRPO), is also designed based on the SSUI dataset to align the MLLM's internal reasoning process with human safety values. Experimental results show that our SRPO-trained models achieve state-of-the-art results on key safety benchmarks, including the proposed Reasoning Path Benchmark (RSBench), significantly outperforming both open-source and top-tier commercial MLLMs.

cs.AI↗

arXiv2025

Non-linear jog-dragging effect on the mobility law of edge dislocations in face-centered cubic nickel

Dislocation jogs have strong effects on dislocation motion that governs the strain-hardening behavior of crystalline solids, but how to properly account for their effect in mesoscale models remains poorly understood. We develop a mobility model for jogged edge dislocations in FCC nickel, based on systematic molecular dynamics (MD) simulations across a range of jog configurations, stresses, and temperatures. At low stresses, jogged edge dislocations exhibit non-linear, thermally activated dragging and a higher Peierls barrier compared to straight dislocations. Surprisingly, stress-velocity curves for a given jog configuration across varying temperatures intersect at an invariant point ($τ_{\rm c}$, $v_{\rm c}$), where $τ_{\rm c}$ delineates thermally-activated and phonon-drag regimes and is close to the Peierls stress ($τ_{\rm p}$). Motivated by this observation, we propose a simple three-section expression for jogged dislocation mobility, featuring minimal and physically interpretable parameters. This mobility law offers a realistic description of jog effects for dislocation dynamics (DD) simulations, improving their physical fidelity for crystal plasticity predictions.

cond-mat.mtrl-sci↗

arXiv2025

ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions

We propose ARDO method for solving PDEs and PDE-related problems with deep learning techniques. This method uses a weak adversarial formulation but transfers the random difference operator onto the test function. The main advantage of this framework is that it is fully derivative-free with respect to the solution neural network. This framework is particularly suitable for Fokker-Planck type second-order elliptic and parabolic PDEs.

math.NA↗

arXiv2025

Large Deviations of First Passage Times of Branching Random Walks in $\mathbb{R}^d$: Asymptotics and Algorithms

We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in $\mathbb{R}^d$ where $d\geq 1$. The FPT refers to the first time the BRW enters a ball of radius one with a distance $x$ from the origin, conditioned upon the process's survival. Furthermore, we apply the spine decomposition technique to construct an asymptotically optimal polynomial-time algorithm for computing the lower large deviation probabilities of the FPT. The accuracy of our algorithm is also verified numerically. Our analysis not only provides a deeper theoretical understanding of these stochastic processes but also offers new insights into the microstructural features that are key to characterizing the strength of polymers.

math.PR↗

arXiv2025

Safe Semantics, Unsafe Interpretations: Tackling Implicit Reasoning Safety in Large Vision-Language Models

Large Vision-Language Models face growing safety challenges with multimodal inputs. This paper introduces the concept of Implicit Reasoning Safety, a vulnerability in LVLMs. Benign combined inputs trigger unsafe LVLM outputs due to flawed or hidden reasoning. To showcase this, we developed Safe Semantics, Unsafe Interpretations, the first dataset for this critical issue. Our demonstrations show that even simple In-Context Learning with SSUI significantly mitigates these implicit multimodal threats, underscoring the urgent need to improve cross-modal implicit reasoning.

cs.AI↗

arXiv2025

Fast multipole method for the Laplace equation in half plane with Robin boundary condition

In this paper, we present a fast multipole method (FMM) for solving the two-dimensional Laplace equation in a half-plane with Robin boundary conditions. The method is based on a novel expansion theory for the reaction component of the Green's function. By applying the Fourier transform, the reaction field component is obtained in a Sommerfeld-type integral form. We derive far-field approximations and corresponding shifting and translation operators from the Fourier integral representation. The FMM for the reaction component is then developed by using the new far-field approximations incorporated into the classic FMM framework in which the tree structure is constructed from the original and image charges. Combining this with the standard FMM for the free-space components, we develop a fast algorithm to compute the interaction of the half plane Laplace Green's function. We prove that the method exhibits exponential convergence, similar to the free-space FMM. Finally, numerical examples are presented to validate the theoretical results and demonstrate that the FMM achieves $O(N)$ computational complexity.

math.NA↗

arXiv2025

Fast Multipole Method for Maxwell's Equations in Layered Media

We present a fast multipole method (FMM) for solving Maxwell's equations in three-dimensional (3-D) layered media, based on the magnetic vector potential $\boldsymbol A$ under the Lorenz gauge, to derive the layered dyadic Green's function. The dyadic Green's function is represented using three scalar Helmholtz layered Green's functions, with all interface-induced reaction field components expressed through a unified integral representation. By introducing equivalent polarization images for sources and effective locations for targets to reflect the actual transmission distance of different reaction field components, multiple expansions (MEs) and local expansions (LEs) are derived for the far-field governed by actual transmission distance. To further enhance computational efficiency and numerical stability, we employ a Chebyshev polynomial expansion of the associated Legendre functions to speed up the calculation of multipole-to-local (M2L) expansion translations. Finally, leveraging the FMM framework of the Helmholtz equation in 3-D layered media, we develop a FMM for the dyadic Green's function of Maxwell's equations in layered media. Numerical experiments demonstrate the $\mathcal O(N\log N)$-complexity of the resulting FMM method, and rapid convergence for interactions of low-frequency electromagnetic wave sources in 3-D layered media.

math.NA↗