Wei Cai

Xuan Zhao, Xiaozhe Hu, Wei Cai et al.

A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical matrices ($\mathcal{H}$-Matrices) for the representation of the stiffness matrix resulting from the finite element discretization of the FDEs. We employ a geometric multigrid method for the solution of the algebraic system of equations. We combine it with an adaptive algorithm based on a posteriori error estimation to deal with general-type singularities arising in the solution of the FDEs. Through various test examples we demonstrate the efficiency of the method and the high-accuracy of the numerical solution even in the presence of singularities. The proposed technique has been verified effectively through fundamental examples including Riesz, Left/Right Riemann-Liouville fractional derivative and, furthermore, it can be readily extended to more general fractional differential equations with different boundary conditions and low-order terms. To the best of our knowledge, there are currently no other methods for FDEs that resolve singularities accurately at linear complexity as the one we propose here.

Jaehong Chung, Rasool Ahmad, WaiChing Sun et al.

This study presents a Graph Neural Networks (GNNs)-based approach for predicting the effective elastic moduli of rocks from their digital CT-scan images. We use the Mapper algorithm to transform 3D digital rock images into graph datasets, encapsulating essential geometrical information. These graphs, after training, prove effective in predicting elastic moduli. Our GNN model shows robust predictive capabilities across various graph sizes derived from various subcube dimensions. Not only does it perform well on the test dataset, but it also maintains high prediction accuracy for unseen rocks and unexplored subcube sizes. Comparative analysis with Convolutional Neural Networks (CNNs) reveals the superior performance of GNNs in predicting unseen rock properties. Moreover, the graph representation of microstructures significantly reduces GPU memory requirements (compared to the grid representation for CNNs), enabling greater flexibility in the batch size selection. This work demonstrates the potential of GNN models in enhancing the prediction accuracy of rock properties and boosting the efficiency of digital rock analysis.

Chanhao Yan, Wei Cai, Xuan Zeng

In this paper, we will present a new approach for solving Laplace equations in general 3-D domains. The approach is based on a local computation method for the DtN mapping of the Laplace equation by combining a deterministic (local) boundary integral equation method and the probabilistic Feynman-Kac formula of PDE solutions. This hybridization produces a parallel algorithm where the bulk of the computation has no need for data communications. Given the Dirichlet data of the solution on a domain boundary, a local boundary integral equation (BIE) will be established over the boundary of a local region formed by a hemisphere superimposed on the domain boundary. By using a homogeneous Dirichlet Green's function for the whole sphere, the resulting BIE will involve only Dirichlet data (solution value) over the hemisphere surface, but over the patch of the domain boundary intersected by the hemisphere, both Dirichlet and Neumann data will be used. Then, firstly, the solution value on the hemisphere surface is computed by the Feynman-Kac formula, which will be implemented by a Monte Carlo walk on spheres (WOS) algorithm. Secondly, a boundary collocation method is applied to solve the integral equation on the aforementioned local patch of the domain boundary to yield the required Neumann data there. As a result, a local method of finding the DtN mapping is obtained, which can be used to find all the Neumann data on the whole domain boundary in a parallel manner. Finally, the potential solution in the whole space can be computed by an integral representation using both the Dirichlet and Neumann data over the domain boundary.

Shaswat Mohanty, Sanghyuk Yoo, Keonwook Kang et al.

Machine-learned force fields have generated significant interest in recent years as a tool for molecular dynamics (MD) simulations, with the aim of developing accurate and efficient models that can replace classical interatomic potentials. However, before these models can be confidently applied to materials simulations, they must be thoroughly tested and validated. The existing tests on the radial distribution function and mean-squared displacements are insufficient in assessing the transferability of these models. Here we present a more comprehensive set of benchmarking tests for evaluating the transferability of machine-learned force fields. We use a graph neural network (GNN)-based force field coupled with the OpenMM package to carry out MD simulations for Argon as a test case. Our tests include computational X-ray photon correlation spectroscopy (XPCS) signals, which capture the density fluctuation at various length scales in the liquid phase, as well as phonon density-of-state in the solid phase and the liquid-solid phase transition behavior. Our results show that the model can accurately capture the behavior of the solid phase only when the configurations from the solid phase are included in the training dataset. This underscores the importance of appropriately selecting the training data set when developing machine-learned force fields. The tests presented in this work provide a necessary foundation for the development and application of machine-learned force fields for materials simulations.

Bo Wanga, Duan Chen, Bo Zhang et al.

In this paper, we develop fast multipole methods for 3D Helmholtz kernel in layered media. Two algorithms based on different forms of Taylor expansion of layered media Green's function are developed. A key component of the first algorithm is an efficient algorithm based on discrete complex image approximation and recurrence formula for the calculation of the layered media Green's function and its derivatives, which are given in terms of Sommerfeld integrals. The second algorithm uses symmetric derivatives in the Taylor expansion to reduce the size of precomputed tables for the derivatives of layered media Green's function. Numerical tests in layered media have validated the accuracy and O(N) complexity of the proposed algorithms.

Min Hyung Cho, Jingfang Huang, Dangxing Chen et al.

In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key compression step in the H-FMM is based on a fact that the multipole expansion for the sources of the free-space Green's function can be used also to compress the far field of the sources of the layered-media or domain Green's function, and a similar result exists for the translation operators for the multipole and local expansions. The mathematical error analysis is shown rigorously by an image representation of the Sommerfeld spectral form of the domain Green's function. As a result, in the H-FMM algorithm, both the "multipole-to-multipole" and "local-to-local" translation operators are the same as those in the free-space case, allowing easy adaptation of existing free-space FMM. All the spatially variant information of the domain Green's function are collected into the "multipole-to-local" translations and therefore the FMM becomes "heterogeneous". The compressed representation further reduces the cost of evaluating the domain Green's function when computing the local direct interactions. Preliminary numerical experiments are presented to demonstrate the efficiency and accuracy of the algorithm with much improved performance over some existing methods for inhomogeneous media. Furthermore, we also show that, due to the equivalence between the complex line image representation and Sommerfeld integral representation of layered media Green's function, the new algorithm can be generalized to multi-layered media with minor modification where details for compression formulas, translation operators, and bookkeeping strategies will be addressed in a subsequent paper.

Yijing Zhou, Wei Cai, Elton Hsu

In this paper, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in R3 and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann boundary condition. Approximations of the RBM based on a walk-on-spheres (WOS) and random walk on lattices are discussed and tested for sampling the RBM paths and their applicability in finding accurate approximation of the local time and discretization of the probabilistic formula. Numerical tests for several types of domains (cube, sphere, and ellipsoid) have shown the convergence of the numerical methods as the length of the RBM path and number of paths sampled increase.

Wei Cai, Jian Wu, Jianguo Xin

In order to solve the magnetohydrodynamics (MHD) equations with a $\mathbf{\mathcal{H}}(\mathbf{div})$-conforming element, a novel approach is proposed to ensure the exact divergence-free condition on the magnetic field. The idea is to add on each element an extra interior bubble function from higher order hierarchical $\mathbf{\mathcal{H}}(\mathbf{div})$-conforming basis. Four such hierarchical bases for the $\mathbf{\mathcal{H}}% (\mathbf{div})$-conforming quadrilateral, triangular, hexahedral and tetrahedral elements are either proposed (in the case of tetrahedral) or reviewed. Numerical results have been presented to show the linear independence of the basis functions for the two simplicial elements. Good matrix conditioning has been confirmed numerically up to the fourth order for the triangular element and up to the third order for the tetrahedral element.

Min Hyung Cho, Wei Cai

Concise and explicit formulas for dyadic Green's functions, representing the electric and magnetic fields due to a dipole source placed in layered media, are derived in this paper. First, the electric and magnetic fields in the spectral domain for the half space are expressed using Fresnel reflection and transmission coefficients. Each component of electric field in the spectral domain constitutes the spectral Green's function in layered media. The Green's function in the spatial domain is then recovered involving Sommerfeld integrals for each component in the spectral domain. By using Bessel identities, the number of Sommerfeld integrals are reduced, resulting in much simpler and more efficient formulas for numerical implementation compared with previous results. This approach is extended to the three-layer Green's function. In addition, the singular part of the Green's function is naturally separated out so that integral equation methods developed for free space Green's functions can be used with minimal modification. Numerical results are included to show efficiency and accuracy of the derived formulas.

Wei Cai, Jun Hu, Shangyou Zhang

In this paper, we will use the interior functions of an hierarchical basis for high order $BDM_p$ elements to enforce the divergence-free condition of a magnetic field $B$ approximated by the H(div) $BDM_p$ basis. The resulting constrained finite element method can be used to solve magnetic induction equation in MHD equations. The proposed procedure is based on the fact that the scalar $(p-1)$-th order polynomial space on each element can be decomposed as an orthogonal sum of the subspace defined by the divergence of the interior functions of the $p$-th order $BDM_p$ basis and the constant function. Therefore, the interior functions can be used to remove element-wise all higher order terms except the constant in the divergence error of the finite element solution of $B$-field. The constant terms from each element can be then easily corrected using a first order H(div) basis globally. Numerical results for a 3-D magnetic induction equation show the effectiveness of the proposed method in enforcing divergence-free condition of the magnetic field.

Wei Peng, Junmei Ding, Wei Wang et al.

Cyber Threat Intelligence (CTI) summarization involves generating concise and accurate highlights from web intelligence data, which is critical for providing decision-makers with actionable insights to swiftly detect and respond to cyber threats in the cybersecurity domain. Despite that, the development of efficient techniques for summarizing CTI reports, comprising facts, analytical insights, attack processes, and more, has been hindered by the lack of suitable datasets. To address this gap, we introduce CTISum, a new benchmark dataset designed for the CTI summarization task. Recognizing the significance of understanding attack processes, we also propose a novel fine-grained subtask: attack process summarization, which aims to help defenders assess risks, identify security gaps, and uncover vulnerabilities. Specifically, a multi-stage annotation pipeline is designed to collect and annotate CTI data from diverse web sources, alongside a comprehensive benchmarking of CTISum using both extractive, abstractive and LLMs-based summarization methods. Experimental results reveal that current state-of-the-art models face significant challenges when applied to CTISum, highlighting that automatic summarization of CTI reports remains an open research problem. The code and example dataset can be made publicly available at https://github.com/pengwei-iie/CTISum.

Wenzhong Zhang, Bo Wang, Wei Cai

In this paper, we will first give a derivation of the multipole expansion (ME) and local expansion (LE) for the far field from sources in general 2-D layered media and the multipole-to-local translation (M2L) operator by using the generating function for Bessel functions. Then, we present a rigorous proof of the exponential convergence of the ME, LE, and M2L for 2-D Helmholtz equations in layered media. It is shown that the convergence of ME, LE, and M2L for the reaction field component of the Green's function depends on a polarized distance between the target and a polarized image of the source.

Yangfan Wang, Tianyang Sun, Chen Tang et al.

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.

Duan Chen, Wei Cai

In this paper, we propose a hierarchical random compression method (HRCM) for kernel matrices in fast kernel summations. The HRCM combines the hierarchical framework of the H-matrix and a randomized sampling technique of the column and row spaces for far-field interaction kernel matrices. We show that a uniform column/row sampling (with a given sample size) of a far-field kernel matrix, with- out the need and associated cost to pre-compute a costly sampling distribution, will give a low-rank compression of such low-rank matrices, independent of the matrix sizes and only dependent on the separation of the source and target locations. This far-field random compression technique is then implemented at each level of the hierarchical decomposition for general kernel matrices, resulting in an O(N logN) random compression method. Error and complexity analysis for the HRCM are included. Numerical results for electrostatic and Helmholtz wave kernels have vali- dated the efficiency and accuracy of the proposed method with a cross-over matrix size, in comparison of direct O(N^2) summations, in the order of thousands for a 3-4 digits relative accuracy.

Yuxiang He, Jian Zhao, Yuchen Yuan et al.

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.

Ye Chen, Wei Cai, Liangmin Wu et al.

We release and introduce the TigerBot family of large language models (LLMs), consisting of base and chat models, sized from 7, 13, 70 and 180 billion parameters. We develop our models embarking from Llama-2 and BLOOM, and push the boundary further in data, training algorithm, infrastructure, and application tools. Our models yield meaningful performance gain over SOTA open-source models, e.g., Llama-2, specifically 6% gain in English and 20% gain in Chinese. TigerBot model family also achieves leading performance in major academic and industrial benchmarks and leaderboards. We believe that TigerBot represents just a snapshot of lightning-fast progression in LLM open-source community. Therefore, we are thrilled to give back by publicly releasing our models and reporting our approach behind, with additional emphases on building SOTA LLMs in a democratized way and making LLMs of use in real-world applications.

Ye Chen, Igor Couto, Wei Cai et al.

We introduce SoftTiger, a clinical large language model (CLaM) designed as a foundation model for healthcare workflows. The narrative and unstructured nature of clinical notes is a major obstacle for healthcare intelligentization. We address a critical problem of structuring clinical notes into clinical data, according to international interoperability standards. We collect and annotate data for three subtasks, namely, international patient summary, clinical impression and medical encounter. We then supervised fine-tuned a state-of-the-art LLM using public and credentialed clinical data. The training is orchestrated in a way that the target model can first support basic clinical tasks such as abbreviation expansion and temporal information extraction, and then learn to perform more complex downstream clinical tasks. Moreover, we address several modeling challenges in the healthcare context, e.g., extra long context window. Our blind pairwise evaluation shows that SoftTiger outperforms other popular open-source models and GPT-3.5, comparable to Gemini-pro, with a mild gap from GPT-4. We believe that LLMs may become a step-stone towards healthcare digitalization and democratization. Therefore, we publicly release SoftTiger models at scales of 13 billion and 70 billion parameters, as well as datasets and code for our innovative scalable evaluation, hopefully, making a significant contribution to the healthcare industry.

Wei Cai, Shujuan Liu, Jian Zhao et al.

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.

Shaswat Mohanty, Yifan Wang, Wei Cai

Machine-learned force fields (MLFFs) promise to offer a computationally efficient alternative to ab initio simulations for complex molecular systems. However, ensuring their generalizability beyond training data is crucial for their wide application in studying solid materials. This work investigates the ability of a graph neural network (GNN)-based MLFF, trained on Lennard-Jones Argon, to describe solid-state phenomena not explicitly included during training. We assess the MLFF's performance in predicting phonon density of states (PDOS) for a perfect face-centered cubic (FCC) crystal structure at both zero and finite temperatures. Additionally, we evaluate vacancy migration rates and energy barriers in an imperfect crystal using direct molecular dynamics (MD) simulations and the string method. Notably, vacancy configurations were absent from the training data. Our results demonstrate the MLFF's capability to capture essential solid-state properties with good agreement to reference data, even for unseen configurations. We further discuss data engineering strategies to enhance the generalizability of MLFFs. The proposed set of benchmark tests and workflow for evaluating MLFF performance in describing perfect and imperfect crystals pave the way for reliable application of MLFFs in studying complex solid-state materials.

Wei Cai, Jian Zhao, Yuchen Yuan et al.

Multimodal Large Language Models (MLLMs), despite their advances, are hindered by their high hallucination tendency and heavy reliance on brittle, linear reasoning processes, leading to failures in complex tasks. To address these limitations, we introduce Visual Attention Reasoning (VAR), a novel framework that recasts grounded reasoning as a structured search over a reasoning trajectory space. VAR decomposes the reasoning process into two key stages: traceable evidence grounding and search-based chain-of-thought (CoT) generation, which incorporates a backtracking mechanism for self-correction. The search is guided by a multi-faceted reward function with semantic and geometric self-verification components, which penalize outputs that are not faithfully grounded in the visual input. We provide a theoretical analysis for our search strategy, validating its capability to find the correct solution with high probability. Experimental results show that our 7B model, VAR-7B, sets a new state-of-the-art on a comprehensive suite of hallucination and safety benchmarks, significantly outperforming existing open-source models and demonstrating competitive performance against leading proprietary systems.

Wei Peng, Lei Cui, Wei Cai et al.

Encrypted traffic classification is the task of identifying the application or service associated with encrypted network traffic. One effective approach for this task is to use deep learning methods to encode the raw traffic bytes directly and automatically extract features for classification (byte-based models). However, current byte-based models input raw traffic bytes, whether plaintext or encrypted text, for automated feature extraction, neglecting the distinct impacts of plaintext and encrypted text on downstream tasks. Additionally, these models primarily focus on improving classification accuracy, with little emphasis on the efficiency of models. In this paper, for the first time, we analyze the impact of plaintext and encrypted text on the model's effectiveness and efficiency. Based on our observations and findings, we propose a two-phase approach to balance the trade-off between plaintext and encrypted text in traffic classification. Specifically, Stage one is to Determine whether the Plain text is enough to be accurately Classified (DPC) using the proposed DPC Selector. This stage quickly identifies samples that can be classified using plaintext, leveraging explicit byte features in plaintext to enhance model's efficiency. Stage two aims to adaptively make a classification with the result from stage one. This stage incorporates encrypted text information for samples that cannot be classified using plaintext alone, ensuring the model's effectiveness on traffic classification tasks. Experiments on two datasets demonstrate that our proposed model achieves state-of-the-art results in both effectiveness and efficiency.

Andrew Qing He, Wei Cai, Sihong Shao

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.

Haihan Duan, Tengfei Ma, Yuyang Qin et al.

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.

Andrew Qing He, Wei Cai

We extend the Weak Adversarial Neural Pushforward Method (WANPM) to the McKean-Vlasov mean-field Fokker-Planck equation. For the quadratic interaction kernel, the mean-field nonlinearity reduces to a batch sample mean, requiring no secondary sampling. We focus on the stationary problem, identifying key training subtleties: gradient flow through the self-consistent mean estimate is essential for uniqueness, and adversarial test function frequencies must be initialized at a sufficiently large scale to avoid spurious minimizers. A numerical benchmark on the 1D linear McKean-Vlasov equation confirms accurate recovery of the exact Gaussian stationary distribution.

Andrew Qing He, Wei Cai

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.

Xinru Hua, Rasool Ahmad, Jose Blanchet et al.

In the field of computational physics and material science, the efficient sampling of rare events occurring at atomic scale is crucial. It aids in understanding mechanisms behind a wide range of important phenomena, including protein folding, conformal changes, chemical reactions and materials diffusion and deformation. Traditional simulation methods, such as Molecular Dynamics and Monte Carlo, often prove inefficient in capturing the timescale of these rare events by brute force. In this paper, we introduce a practical approach by combining the idea of importance sampling with deep neural networks (DNNs) that enhance the sampling of these rare events. In particular, we approximate the variance-free bias potential function with DNNs which is trained to maximize the probability of rare event transition under the importance potential function. This method is easily scalable to high-dimensional problems and provides robust statistical guarantees on the accuracy of the estimated probability of rare event transition. Furthermore, our algorithm can actively generate and learn from any successful samples, which is a novel improvement over existing methods. Using a 2D system as a test bed, we provide comparisons between results obtained from different training strategies, traditional Monte Carlo sampling and numerically solved optimal bias potential function under different temperatures. Our numerical results demonstrate the efficacy of the DNN-based importance sampling of rare events.

Wei Cai, Jian Zhao, Yuchu Jiang et al.

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.

Bo Wang, Lizuo Liu, Wei Cai

In this paper, a multi-scale DeepOnet (Mscale-DeepOnet) is proposed to reduce the spectral bias of the DeepOnet in learning high-frequency mapping between highly oscillatory functions, with an application to the nonlinear mapping between the coefficient of the Helmholtz equation and its solution. The Mscale-DeepOnet introduces the multiscale neural network in the branch and trunk networks of the original DeepOnet, the resulting Mscale-DeepOnet is shown to be able to capture various high-frequency components of the mapping itself and its image. Numerical results demonstrate the substantial improvement of the Mscale-DeepOnet for the problem of wave scattering in the high-frequency regime over the normal DeepOnet with a similar number of network parameters.

Wenzhong Zhang, Zhenyuan Hu, Wei Cai et al.

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.

Andrew Qing He, Wei Cai

We extend the Weak Adversarial Neural Pushforward Method (WANPM) to fractional Fokker-Planck equations (fFPE), in which the classical Laplacian diffusion operator is replaced by the fractional Laplacian $(-Δ)^{α/2}$ for $α\in (0, 2]$. The solution distribution is represented not as an explicit probability density function but as the pushforward of a simple base distribution through a time-parameterized neural network $F_\vartheta(t, x_0, r)$, which enforces the initial condition exactly by construction. The weak formulation of the fFPE is discretized via Monte Carlo sampling entirely without temporal discretization, and the resulting min-max objective is optimized adversarially against a set of plane-wave test functions. A key computational advantage is that plane waves are eigenfunctions of the fractional Laplacian, so $(-Δ_x)^{α/2} f = |w|^αf$ is computed exactly and at no additional cost for any $α$. We validate the method on a one-dimensional fractional Fokker-Planck equation with a quadratic confining potential and $α= 1.5$, using a particle simulation based on symmetric $α$-stable Levy increments as a benchmark. The learned solution faithfully reproduces the transient probability distribution over $t \in [0, 2]$, and robust statistics confirm close agreement with the particle simulation, while standard deviation comparisons highlight why second-moment metrics are inappropriate for heavy-tailed ($α< 2$) distributions.

Wei Cai, Andrew Qing He

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.

Jaehong Chung, Wei Cai, Tapan Mukerji

This study proposes a systematic image registration approach to align 2D optical thin-section images within a 3D digital rock volume. Using template image matching with differential evolution optimization, we identify the most similar 2D plane in 3D. The method is validated on a synthetic porous medium, achieving exact registration, and applied to Berea sandstone, where it achieves a structural similarity index (SSIM) of 0.990. With the registered images, we explore upscaling properties based on paired multimodal images, focusing on pore characteristics and effective elastic moduli. The thin-section image reveals 50 % more porosity and submicron pores than the registered CT plane. In addition, bulk and shear moduli from thin sections are 25 % and 30 % lower, respectively, than those derived from CT images. Beyond numerical comparisons, thin sections provide additional geological insights, including cementation, mineral phases, and weathering effects, which are not clear in CT images. This study demonstrates the potential of multimodal image registration to improve computed rock properties in digital rock physics by integrating complementary imaging modalities.

Yuchuan Jiang, Chaolong Jia, Yunyi Qin et al.

The rapid proliferation of the Internet and the widespread adoption of social networks have significantly accelerated information dissemination. However, this transformation has introduced complexities in information capture and processing, posing substantial challenges for researchers and practitioners. Predicting the dissemination of topic-related information within social networks has thus become a critical research focus. This paper proposes a predictive model for topic dissemination in social networks by integrating multidimensional features derived from key dissemination characteristics. Specifically, we introduce two novel indicators, user relationship breadth and user authority, into the PageRank algorithm to quantify user influence more effectively. Additionally, we employ a Text-CNN model for sentiment classification, extracting sentiment features from textual content. Temporal embeddings of nodes are encoded using a Bi-LSTM model to capture temporal dynamics. Furthermore, we refine the measurement of user interaction traces with topics, replacing traditional topic view metrics with a more precise communication characteristics measure. Finally, we integrate the extracted multidimensional features using a Transformer model, significantly enhancing predictive performance. Experimental results demonstrate that our proposed model outperforms traditional machine learning and unimodal deep learning models in terms of FI-Score, AUC, and Recall, validating its effectiveness in predicting topic propagation within social networks.

Lehao Lin, Ke Wang, Maha Abdallah et al.

In recent years, the rapid development of artificial intelligence (AI) especially multi-modal Large Language Models (MLLMs), has enabled it to understand text, images, videos, and other multimedia data, allowing AI systems to execute various tasks based on human-provided prompts. However, AI-powered bots have increasingly been able to bypass most existing CAPTCHA systems, posing significant security threats to web applications. This makes the design of new CAPTCHA mechanisms an urgent priority. We observe that humans are highly sensitive to shifts and abrupt changes in videos, while current AI systems still struggle to comprehend and respond to such situations effectively. Based on this observation, we design and implement BounTCHA, a CAPTCHA mechanism that leverages human perception of boundaries in video transitions and disruptions. By utilizing generative AI's capability to extend original videos with prompts, we introduce unexpected twists and changes to create a pipeline for generating guided short videos for CAPTCHA purposes. We develop a prototype and conduct experiments to collect data on humans' time biases in boundary identification. This data serves as a basis for distinguishing between human users and bots. Additionally, we perform a detailed security analysis of BounTCHA, demonstrating its resilience against various types of attacks. We hope that BounTCHA will act as a robust defense, safeguarding millions of web applications in the AI-driven era.

Qing He, Wei Cai

We propose a deep neural network architecture designed such that its output forms an invertible symplectomorphism of the input. This design draws an analogy to the real-valued non-volume-preserving (real NVP) method used in normalizing flow techniques. Utilizing this neural network type allows for learning tasks on unknown Hamiltonian systems without breaking the inherent symplectic structure of the phase space.

Haihan Duan, Jiaye Li, Sizheng Fan et al.

In recent years, the metaverse has attracted enormous attention from around the world with the development of related technologies. The expected metaverse should be a realistic society with more direct and physical interactions, while the concepts of race, gender, and even physical disability would be weakened, which would be highly beneficial for society. However, the development of metaverse is still in its infancy, with great potential for improvement. Regarding metaverse's huge potential, industry has already come forward with advance preparation, accompanied by feverish investment, but there are few discussions about metaverse in academia to scientifically guide its development. In this paper, we highlight the representative applications for social good. Then we propose a three-layer metaverse architecture from a macro perspective, containing infrastructure, interaction, and ecosystem. Moreover, we journey toward both a historical and novel metaverse with a detailed timeline and table of specific attributes. Lastly, we illustrate our implemented blockchain-driven metaverse prototype of a university campus and discuss the prototype design and insights.

Ziqi Liu, Wei Cai, Zhi-Qin John Xu

In this paper, we propose multi-scale deep neural networks (MscaleDNNs) using the idea of radial scaling in frequency domain and activation functions with compact support. The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to a problem of learning about lower frequency functions, and the compact support activation functions facilitate the separation of frequency contents of the target function to be approximated by corresponding DNNs. As a result, the MscaleDNNs achieve fast uniform convergence over multiple scales. The proposed MscaleDNNs are shown to be superior to traditional fully connected DNNs and be an effective mesh-less numerical method for Poisson-Boltzmann equations with ample frequency contents over complex and singular domains.

Wei Cai, Zhi-Qin John Xu

In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs. Numerical results on high dimensional function fitting and solutions of high dimensional PDEs, using loss functions with either Ritz energy or least squared PDE residuals, have validated the increased power of multi-scale resolution and high frequency capturing of the proposed MscaleDNN.

Wei Cai, Xiaoguang Li, Lizuo Liu

In this paper, we propose a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wave equations. The PhaseDNN makes use of the fact that common DNNs often achieve convergence in the low frequency range first, and a series of moderately-sized DNNs are constructed and trained for selected high frequency ranges. With the help of phase shifts in the frequency domain, each of the DNNs will be trained to approximate the function's higher frequency content over a specific range at the the speed of convergence as in the low frequency range. As a result, the proposed PhaseDNN is able to convert high frequency learning to low frequency one, allowing a uniform learning to wideband functions. The PhaseDNN will then be applied to find the solution of high frequency wave equations in inhomogeneous media through both differential and integral equation formulations with least square residual loss functions. Numerical results have demonstrated the capability of the PhaseDNN in learning high frequency functions and oscillatory solutions of interior and exterior Helmholtz equations.

Tengfei Wang, Shuyi Zhang, Xiao Wu et al.

Rhythm Dungeon is a rhythm game which leverages the blockchain as a shared open database. During the gaming session, the player explores a roguelike dungeon by inputting specific sequences in time to music rhythm. By integrating smart contract to the game program, the enemies through the venture are generated from other games which share the identical blockchain. On the other hand, the player may upload their characters at the end of their journey, so that their own character may appear in other games and make an influence. Rhythm Dungeon is designed and implemented to show the potential of decentralized gaming experience, which utilizes the blockchain to provide asynchronous interactions among massive players.

Tian Min, Hanyi Wang, Yaoze Guo et al.

With the support of the blockchain systems, the cryptocurrency has changed the world of virtual assets. Digital games, especially those with massive multi-player scenarios, will be significantly impacted by this novel technology. However, there are insufficient academic studies on this topic. In this work, we filled the blank by surveying the state-of-the-art blockchain games. We discuss the blockchain integration for games and then categorize existing blockchain games from the aspects of their genres and technical platforms. Moreover, by analyzing the industrial trend with a statistical approach, we envision the future of blockchain games from technological and commercial perspectives.

Tian Min, Wei Cai

Blockchain gaming is an emerging entertainment paradigm. However, blockchain games are still suffering from security issues, due to the immature blockchain technologies and its unsophisticated developers. In this work, we analyzed the blockchain game architecture and reveal the possible penetration methods of cracking. We scanned more than 600 commercial blockchain games to summarize a security overview from the perspective of the web server and smart contract, respectively. We also conducted three case studies for blockchain games to show detailed vulnerability detection.

Wei Cai, Xiaoguang Li, Lizuo Liu

In this paper, we propose a phase shift deep neural network (PhaseDNN) which provides a wideband convergence in approximating a high dimensional function during its training of the network. The PhaseDNN utilizes the fact that many DNN achieves convergence in the low frequency range first, thus, a series of moderately-sized of DNNs are constructed and trained in parallel for ranges of higher frequencies. With the help of phase shifts in the frequency domain, implemented through a simple phase factor multiplication on the training data, each DNN in the series will be trained to approximate the target function's higher frequency content over a specific range. Due to the phase shift, each DNN achieves the speed of convergence as in the low frequency range. As a result, the proposed PhaseDNN system is able to convert wideband frequency learning to low frequency learning, thus allowing a uniform learning to wideband high dimensional functions with frequency adaptive training. Numerical results have demonstrated the capability of PhaseDNN in learning information of a target function from low to high frequency uniformly.

Wei Cai, Zehua Wang, Jason B. Ernst et al.

Blockchain technology has attracted tremendous attention in both academia and capital market. However, overwhelming speculations on thousands of available cryptocurrencies and numerous initial coin offering (ICO) scams have also brought notorious debates on this emerging technology. This paper traces the development of blockchain systems to reveal the importance of decentralized applications (dApps) and the future value of blockchain. We survey the state-of-the-art dApps and discuss the direction of blockchain development to fulfill the desirable characteristics of dApps. The readers will gain an overview of dApp research and get familiar with recent developments in the blockchain.

Duan Chen, Wei Cai, Brian Zinser et al.

In this paper, we develop an accurate and efficient Nyström volume integral equation (VIE) method for the Maxwell equations for large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for several objects, such as cubes and spheres, that are frequently encountered in the design of meta-materials . The resulting Nyström VIE method is shown to have high accuracy with a minimum number of collocation points and demonstrate $p$-convergence for computing the electromagnetic scattering of these objects. Numerical calculations of multiple scatterers of cubic and spherical shapes validate the efficiency and accuracy of the proposed method.

Duan Chen, Wei Cai, Brian Zinser

In this paper, we develop highly accurate Nyström methods for the volume integral equation (VIE) of the Maxwell equation for 3-D scatters. The method is based on a formulation of the VIE equation where the Cauchy principal value of the dyadic Green's function can be computed accurately for a finite size exclusion volume with some explicit corrective integrals of removable singularities. Then, an effective interpolated quadrature formula for tensor product Gauss quadrature nodes in a cube is proposed to handle the hyper-singularity of integrals of the dyadic Green's function. The proposed high order Nyström VIE method is shown to have high accuracy and demonstrates $p$-convergence for computing the electromagnetic scattering of cubes in $R^3$.

Yijing Zhou, Wei Cai

In this paper, we present numerical methods to implement the probabilistic representation of third kind (Robin) boundary problem for the Laplace equations. The solution is based on a Feynman-Kac formula for the Robin problem which employs the standard reflecting Brownian motion (SRBM) and its boundary local time arising from the Skorohod problem. By simulating SRBM paths through Brownian motion using Walk on Spheres (WOS) method, approximation of the boundary local time is obtained and the Feynman-Kac formula is calculated by evaluating the average of all path integrals over the boundary under a measure defined through the local time. Numerical results demonstrate the accuracy and efficiency of the proposed method for finding a local solution of the Laplace equations with Robin boundary conditions.