arXiv subjects

Wei Cai

Publications and source records attributed to Wei Cai.

At least 19 recordsLinked to original sources

arXiv2026

Weak Adversarial Neural Pushforward Method for Boltzmann Equation

In this paper, we extend a weak adversary neural network pushforward method for solving time dependent Boltzmann equation and a weak formulation of the collision operator is proposed where an invertible neural pushforward mapping is used to generating samples given by the distribution governed by the Boltzmann equation. The training of the pushforward mapping is learnt by enforcing the weak form of the Boltzmann equation. Numerical results have demonstrated the effectiveness of the proposed method.

math.NA↗

arXiv2026

Neuro-Symbolic Participation Governance for Verifiable AI Agents in Open Digital Twin Ecosystems

Autonomous AI agents, increasingly empowered by large language models, are becoming important components of human-machine systems for high-stakes decision support in digital twin ecosystems. However, existing multi-agent systems often lack robust verification for identity, capability, and policy compliance, especially in decentralized environments spanning multiple institutions. This paper proposes a neuro-symbolic decentralized governance framework for verifiable agents in collaborative digital twin environments. By representing agents through multi-layer semantic profiles, the framework bridges probabilistic neural reasoning with deterministic institutional governance, thereby supporting trustworthy human-AI collaboration and meaningful human oversight. Capabilities are grounded in formal domain ontologies to enable machine-interpretable, policy-aware, and context-sensitive participation. These credentials, issued by organizational authorities, are validated via blockchain-based smart contracts, ensuring auditable participation without exposing sensitive data. We demonstrate the framework using a decision-support prototype with clinic, digital twin, and wearable provider agents effectively prevents unauthorized interaction and enforces institutional policies with manageable overhead. Our findings suggest that neuro-symbolic decentralized governance provides a scalable and trustworthy pathway for safe human-machine collaboration across institutional boundaries.

cs.CR↗

arXiv2026

A convolutional neural network surrogate for hierarchical homogenization: fast elastic moduli prediction of digital rocks

Digital rock physics (DRP) aims to estimate effective rock properties (e.g., elastic moduli) directly from 3D micro-CT images. However, direct numerical simulations (DNS) on high-resolution large 3D scans are often computationally prohibitive and severely limit the application of DRP. To address this bottleneck, we combine a lightweight 3D convolutional neural network (CNN) with hierarchical homogenization (HHM) and apply it to determine effective elastic moduli. In this scheme, a large rock image is divided into subcubes. The CNN replaces costly DNS by directly predicting subcube elastic moduli, while HHM upscales subcube-level predictions to the full rock. Using a shared convolutional backbone, we systematically compare three training targets: (i) full anisotropic $6\times6$ stiffness tensors, (ii) isotropic bulk and shear moduli $(K, G)$, and (iii) Hashin--Shtrikman (HS)-normalized factors. Across multiple rock types, all three models agree well with DNS results while substantially reducing the computational cost. Moreover, training from scratch on each rock type is fast enough that transfer learning is unnecessary. Across all three targets, the accuracy is comparable. In our comparative study, the HS-normalized factor offers the best overall speed--accuracy trade-off while guaranteeing physical consistency, making it a convenient default. The isotropic $(K, G)$ target is a slightly more accurate alternative.

physics.comp-ph↗

arXiv2026

Multiscale Fourier Neural Operator for Inverse Wave Scattering in Highly Oscillatory Media

In this paper, we propose an operator learning method based on the multiscale Fourier neural operator (MscaleFNO) for inverse medium problems of Helmholtz equations. The MscaleFNO provides a neural surrogate model with reduced spectral bias for the Helmholtz equations, mapping highly oscillatory medium profiles to scattered wavefields. A plug-and-play inversion using elucidated diffusion model is introduced to regularize the inverse solver based on least squares of data misfits. Numerical results for partial aperture inversion of oscillatory two-dimensional media demonstrate the advantage and effectiveness of MscaleFNO for accurate reconstruction of highly oscillatory medium properties.

math.NA↗

arXiv2026

Crystal Dislocations as Atomic Scale Ratchets

The symmetry of a system's response to external stimuli is a fundamental concept in physics and materials science. At the microscopic scale, breaking this symmetry to achieve a rectified response is exceptionally difficult to engineer and remains rare in nature. Conventional micromechanics models of crystalline solids assume a symmetric response to applied stress, where reversing the load simply inverts the direction of defect velocity without altering its magnitude. In this work, we report an atomic-scale, geometry-rooted mechanism that breaks this symmetry. Molecular dynamics simulations of face-centered cubic nickel reveal that dislocations containing atomic-scale jogs exhibit asymmetric mobility under opposite applied stresses, reversing the loading direction triggers significantly higher drag. This asymmetry arises from an unconventional coupling between an atomic displacement vector and the second-order tensorial eigenstrain of the jog motion mechanism. Because jogs are ubiquitous structures in plastic deformation, this discovery challenges classical descriptions of plastic deformation mechanisms, with direct implications to cyclic creep, and opens new pathways for defect engineering to enhance fatigue resistance.

cond-mat.mtrl-sci↗

arXiv2026

DeRelayL: Sustainable Decentralized Relay Learning

In the era of big data, large-scale machine learning models have revolutionized various fields, driving significant advancements. However, large-scale model training demands high financial and computational resources, which are only affordable by a few technological giants and well-funded institutions. In this case, common users like mobile users, the real creators of valuable data, are often excluded from fully benefiting due to the barriers, while the current methods for accessing large-scale models either limit user ownership or lack sustainability. This growing gap highlights the urgent need for a collaborative model training approach, allowing common users to train and share models. However, existing collaborative model training paradigms, especially federated learning (FL), primarily focus on data privacy and group-based model aggregation. To this end, this paper intends to address this issue by proposing a novel training paradigm named decentralized relay learning (DeRelayL), a sustainable learning system where permissionless participants can contribute to model training in a relay-like manner and share the model. In detail, this paper presents the architecture and workflow of DeRelayL, designs incentive mechanisms to ensure sustainability, and conducts theoretical analysis and numerical simulations to demonstrate its effectiveness.

cs.LG↗

arXiv2026

HiEdit: Lifelong Model Editing with Hierarchical Reinforcement Learning

Lifelong model editing (LME) aims to sequentially rectify outdated or inaccurate knowledge in deployed LLMs while minimizing side effects on unrelated inputs. However, existing approaches typically apply parameter perturbations to a static and dense set of LLM layers for all editing instances. This practice is counter-intuitive, as we hypothesize that different pieces of knowledge are stored in distinct layers of the model. Neglecting this layer-wise specificity can impede adaptability in integrating new knowledge and result in catastrophic forgetting for both general and previously edited knowledge. To address this, we propose HiEdit, a hierarchical reinforcement learning framework that adaptively identifies the most knowledge-relevant layers for each editing instance. By enabling dynamic, instance-aware layer selection and incorporating an intrinsic reward for sparsity, HiEdit achieves precise, localized updates. Experiments on various LLMs show that HiEdit boosts the performance of the competitive RLEdit by an average of 8.48% with perturbing only half of the layers per edit. Our code is available at: https://github.com/yangfanww/hiedit.

cs.CL↗

arXiv2026

Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation

We extend the Weak Adversarial Neural Pushforward Method to the Wigner transport equation governing the phase-space dynamics of quantum systems. The central contribution is a structural observation: integrating the nonlocal pseudo-differential potential operator against plane-wave test functions produces a Dirac delta that exactly inverts the Fourier transform defining the Wigner potential kernel, reducing the operator to a pointwise finite difference of the potential at two shifted arguments. This holds in arbitrary dimension, requires no truncation of the Moyal series, and treats the potential as a black-box function oracle with no derivative information. To handle the negativity of the Wigner quasi-probability distribution, we introduce a signed pushforward architecture that decomposes the solution into two non-negative phase-space distributions mixed with a learnable weight. The resulting method inherits the mesh-free, Jacobian-free, and scalable properties of the original framework while extending it to the quantum setting.

quant-ph↗

arXiv2026

Learning Interatomic Force Coefficients from X-ray Thermal Diffuse Scattering Data

We present a fully automated framework for extracting interatomic force constants (IFCs) directly from X-ray thermal diffuse scattering (TDS) data. By formulating scattering intensity as a differentiable function of a symmetry-reduced IFC parameterization, we enable gradient-based optimization via direct, Cholesky-based sampling of correlated atomic displacements at thermal equilibrium. This approach bypasses the computational bottleneck of repeated Hessian matrix diagonalizations, significantly accelerating the inversion process. Benchmark tests demonstrate that the framework accurately recovers ground-truth IFCs and phonon dispersion relations, providing a robust, high-throughput pathway for studying lattice dynamics across diverse crystalline materials. This method bridges the gap between experimental observations and computational modeling, enabling the direct integration of TDS data into the refinement of high-fidelity inter-atomic potentials.

physics.comp-ph↗

arXiv2026

Weak Adversarial Neural Pushforward Method for the McKean-Vlasov / Mean-Field Fokker-Planck Equation

We extend the Weak Adversarial Neural Pushforward Method (WANPM) to the McKean--Vlasov mean-field Fokker--Planck equation, covering both the stationary and time-dependent cases. The key observation is that the mean-field nonlinearity -- an expectation under the solution distribution -- is naturally estimated by Monte Carlo sampling from the pushforward network, requiring no change to the architecture and only minor modifications to the training loop. For the quadratic (granular media) interaction kernel, the interaction term reduces to the batch sample mean, eliminating secondary sampling entirely. We also identify a dimension-dependent frequency initialization rule for the adversarial test functions, necessary to avoid spurious minimizers. Numerical experiments on linear McKean--Vlasov benchmarks in 2, 5, 20, and 100 dimensions confirm accurate recovery of the exact Gaussian stationary and transient distributions, with training times ranging from 27 seconds (2D) to 10 minutes (100D) on a single GPU.

math.NA↗

arXiv2026

Neural Pushforward Samplers for the Fokker-Planck Equation on Embedded Riemannian Manifolds

In this paper, we extend the Weak Adversarial Neural Pushforward Method to the Fokker--Planck equation on compact embedded Riemannian manifolds. The method represents the solution as a probability distribution via a neural pushforward map that is constrained to the manifold by a retraction layer, enforcing manifold membership and probability conservation by construction. Training is guided by a weak adversarial objective using ambient plane-wave test functions, whose intrinsic differential operators are derived in closed form from the geometry of the embedding, yielding a fully mesh-free and chart-free algorithm. Both steady-state and time-dependent formulations are developed, and numerical results on a double-well problem on the two-sphere demonstrate the capability of the method in capturing multimodal invariant distributions on curved spaces.

math.NA↗

arXiv2026

Weak Adversarial Neural Pushforward Method for Fractional Fokker-Planck Equations

We extend the Weak Adversarial Neural Pushforward Method (WANPM) to fractional Fokker-Planck equations, in which the classical Laplacian diffusion operator is replaced by the fractional Laplacian of order alpha in (0, 2]. The solution distribution is represented as the pushforward of a simple base distribution through a neural network, and the weak formulation is discretized entirely via Monte Carlo sampling without any temporal mesh. A key computational advantage is that plane-wave test functions are eigenfunctions of the fractional Laplacian, making the operator cost identical to that of classical diffusion for any alpha. We validate the method on seven benchmark problems with alpha = 1.5, spanning one and two spatial dimensions: the steady-state fractional Ornstein--Uhlenbeck (OU) process, a harmonic confining potential, a double-well potential, and a triple-well potential in one dimension, a steady-state 2D double-peak distribution, a time-dependent 2D ring distribution with rotational drift, and a five-dimensional harmonic potential. Each case is benchmarked against particle simulations using symmetric alpha-stable L\'evy increments, and robust statistics confirm close agreement throughout. The method is mesh-free, requires no density evaluation or non-local quadrature, and provides a promising foundation for high-dimensional anomalous diffusion solvers.

math.NA↗

arXiv2026

From Connectivity to Rupture: A Coarse-Grained Stochastic Network Dynamics Approach to Polymer Network Mechanics

We introduce a coarse-grained stochastic network dynamics (CGSND) framework for modeling deformation and rupture in polymer networks. The method replaces explicit molecular dynamics (MD) or coarse-grained molecular dynamics (CGMD) with network-level evolution rules while retaining chain entropic elasticity and force-controlled bond failure. Under uniaxial loading, CGSND reproduces the characteristic nonlinear stress--stretch response of elastomeric networks, including a well-defined ultimate tensile strength and post-peak softening due to progressive bond rupture. Comparison with coarse-grained molecular dynamics (CGMD) simulations shows that CGSND captures the qualitative form of the stress response and the onset of catastrophic damage despite its rate-independent formulation. Analysis of rupture kinetics reveals a pronounced peak in the bond-breaking hazard rate near the ultimate tensile strength in both approaches. In addition, the distribution of broken segment lengths remains statistically indistinguishable from the initial network, indicating that rupture is not biased toward short or long chains. Finally, the evolution of the Gini coefficient of bond force magnitudes reveals strong force localization preceding failure. These results demonstrate that CGSND provides a computationally efficient and physically interpretable framework for connecting force localization and rupture kinetics to macroscopic failure in polymer networks.

cond-mat.soft↗

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

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↗

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

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

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 Nystr\"{o}m 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↗