arXiv subjects

Ran Zhang

Publications and source records attributed to Ran Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2025

Pressure-robustness in Stokes-Darcy Optimal Control Problem with reconstruction operator

This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement of normal continuity at interfaces, within the framework of the mixed finite element method (FEM). The methodology involves the strategic deployment of a reconstruction operator, which is adeptly applied to both the constraint equations and the cost functional. This is complemented by a judicious selection of finite element spaces that are tailored for approximation and reconstruction purposes. The synergy of these methodological choices leads to the realization of a discretization scheme that is pressure-robust, thereby enhancing the robustness and reliability of numerical simulations in computational mathematics.

math.NA↗

arXiv2025

Integrating Reinforcement Learning and AI Agents for Adaptive Robotic Interaction and Assistance in Dementia Care

This study explores a novel approach to advancing dementia care by integrating socially assistive robotics, reinforcement learning (RL), large language models (LLMs), and clinical domain expertise within a simulated environment. This integration addresses the critical challenge of limited experimental data in socially assistive robotics for dementia care, providing a dynamic simulation environment that realistically models interactions between persons living with dementia (PLWDs) and robotic caregivers. The proposed framework introduces a probabilistic model to represent the cognitive and emotional states of PLWDs, combined with an LLM-based behavior simulation to emulate their responses. We further develop and train an adaptive RL system enabling humanoid robots, such as Pepper, to deliver context-aware and personalized interactions and assistance based on PLWDs' cognitive and emotional states. The framework also generalizes to computer-based agents, highlighting its versatility. Results demonstrate that the RL system, enhanced by LLMs, effectively interprets and responds to the complex needs of PLWDs, providing tailored caregiving strategies. This research contributes to human-computer and human-robot interaction by offering a customizable AI-driven caregiving platform, advancing understanding of dementia-related challenges, and fostering collaborative innovation in assistive technologies. The proposed approach has the potential to enhance the independence and quality of life for PLWDs while alleviating caregiver burden, underscoring the transformative role of interaction-focused AI systems in dementia care.

cs.AI↗

arXiv2025

A Moving Mesh Isogeometric Method Based on Harmonic Maps

Although the isogeometric analysis has shown its great potential in achieving highly accurate numerical solutions of partial differential equations, its efficiency is the main factor making the method more competitive in practical simulations. In this paper, an integration of isogeometric analysis and a moving mesh method is proposed, providing a competitive approach to resolve the efficiency issue. Focusing on the Poisson equation, the implementation of the algorithm and related numerical analysis are presented in detail, including the numerical discretization of the governing equation utilizing isogeometric analysis, and a mesh redistribution technique developed via harmonic maps. It is found that the isogeometric analysis brings attractive features in the realization of moving mesh method, such as it provides an accurate expression for moving direction of mesh nodes, and allows for more choices for constructing monitor functions. Through a series of numerical experiments, the effectiveness of the proposed method is successfully validated and the potential of the method towards the practical application is also well presented with the simulation of a helium atom in Kohn--Sham density functional theory.

math.NA↗

arXiv2025

Probabilistic Greedy Algorithm Solver Using Magnetic Tunneling Junctions for Traveling Salesman Problem

Combinatorial optimization problems are foundational challenges in fields such as artificial intelligence, logistics, and network design. Traditional algorithms, including greedy methods and dynamic programming, often struggle to balance computational efficiency and solution quality, particularly as problem complexity scales. To overcome these limitations, we propose a novel and efficient probabilistic optimization framework that integrates true random number generators (TRNGs) based on spin-transfer torque magnetic tunneling junctions (STT-MTJs). The inherent stochastic switching behavior of STT-MTJs enables dynamic configurability of random number distributions, which we leverage to introduce controlled randomness into a probabilistic greedy algorithm. By tuning a temperature parameter, our algorithm seamlessly transitions between deterministic and stochastic strategies, effectively balancing exploration and exploitation. Furthermore, we apply this framework to the traveling salesman problem (TSP), showcasing its ability to consistently produce high-quality solutions across diverse problem scales. Our algorithm demonstrates superior performance in both solution quality and convergence speed compared to classical approaches, such as simulated annealing and genetic algorithms. Specifically, in larger TSP instances involving up to 70 cities, it retains its performance advantage, achieving near-optimal solutions with fewer iterations and reduced computational costs. This work highlights the potential of integrating MTJ-based TRNGs into optimization algorithms, paving the way for future applications in probabilistic computing and hardware-accelerated optimization.

physics.app-ph↗

arXiv2025

Orthogonal greedy algorithm for linear operator learning with shallow neural network

Greedy algorithms, particularly the orthogonal greedy algorithm (OGA), have proven effective in training shallow neural networks for fitting functions and solving partial differential equations (PDEs). In this paper, we extend the application of OGA to the tasks of linear operator learning, which is equivalent to learning the kernel function through integral transforms. Firstly, a novel greedy algorithm is developed for kernel estimation rate in a new semi-inner product, which can be utilized to approximate the Green's function of linear PDEs from data. Secondly, we introduce the OGA for point-wise kernel estimation to further improve the approximation rate, achieving orders of accuracy improvement across various tasks and baseline models. In addition, we provide a theoretical analysis on the kernel estimation problem and the optimal approximation rates for both algorithms, establishing their efficacy and potential for future applications in PDEs and operator learning tasks.

math.NA↗

arXiv2024

A hierarchical splines-based $h$-adaptive isogeometric solver for all-electron Kohn--Sham equation

In this paper, a novel $h$-adaptive isogeometric solver utilizing high-order hierarchical splines is proposed to solve the all-electron Kohn--Sham equation. In virtue of the smooth nature of Kohn--Sham wavefunctions across the domain, except at the nuclear positions, high-order globally regular basis functions such as B-splines are well suited for achieving high accuracy. To further handle the singularities in the external potential at the nuclear positions, an $h$-adaptive framework based on the hierarchical splines is presented with a specially designed residual-type error indicator, allowing for different resolutions on the domain. The generalized eigenvalue problem raising from the discretized Kohn--Sham equation is effectively solved by the locally optimal block preconditioned conjugate gradient (LOBPCG) method with an elliptic preconditioner, and it is found that the eigensolver's convergence is independent of the spline basis order. A series of numerical experiments confirm the effectiveness of the $h$-adaptive framework, with a notable experiment that the numerical accuracy $10^{-3} \mathrm{~Hartree/particle}$ in the all-electron simulation of a methane molecule is achieved using only $6355$ degrees of freedom, demonstrating the competitiveness of our solver for the all-electron Kohn--Sham equation.

physics.comp-ph↗

arXiv2024

NLLG Quarterly arXiv Report 09/24: What are the most influential current AI Papers?

The NLLG (Natural Language Learning & Generation) arXiv reports assist in navigating the rapidly evolving landscape of NLP and AI research across cs.CL, cs.CV, cs.AI, and cs.LG categories. This fourth installment captures a transformative period in AI history - from January 1, 2023, following ChatGPT's debut, through September 30, 2024. Our analysis reveals substantial new developments in the field - with 45% of the top 40 most-cited papers being new entries since our last report eight months ago and offers insights into emerging trends and major breakthroughs, such as novel multimodal architectures, including diffusion and state space models. Natural Language Processing (NLP; cs.CL) remains the dominant main category in the list of our top-40 papers but its dominance is on the decline in favor of Computer vision (cs.CV) and general machine learning (cs.LG). This report also presents novel findings on the integration of generative AI in academic writing, documenting its increasing adoption since 2022 while revealing an intriguing pattern: top-cited papers show notably fewer markers of AI-generated content compared to random samples. Furthermore, we track the evolution of AI-associated language, identifying declining trends in previously common indicators such as "delve".

cs.DL↗

arXiv2024

Maximizing User Connectivity in AI-Enabled Multi-UAV Networks: A Distributed Strategy Generalized to Arbitrary User Distributions

Deep reinforcement learning (DRL) has been extensively applied to Multi-Unmanned Aerial Vehicle (UAV) network (MUN) to effectively enable real-time adaptation to complex, time-varying environments. Nevertheless, most of the existing works assume a stationary user distribution (UD) or a dynamic one with predicted patterns. Such considerations may make the UD-specific strategies insufficient when a MUN is deployed in unknown environments. To this end, this paper investigates distributed user connectivity maximization problem in a MUN with generalization to arbitrary UDs. Specifically, the problem is first formulated into a time-coupled combinatorial nonlinear non-convex optimization with arbitrary underlying UDs. To make the optimization tractable, a multi-agent CNN-enhanced deep Q learning (MA-CDQL) algorithm is proposed. The algorithm integrates a ResNet-based CNN to the policy network to analyze the input UD in real time and obtain optimal decisions based on the extracted high-level UD features. To improve the learning efficiency and avoid local optimums, a heatmap algorithm is developed to transform the raw UD to a continuous density map. The map will be part of the true input to the policy network. Simulations are conducted to demonstrate the efficacy of UD heatmaps and the proposed algorithm in maximizing user connectivity as compared to K-means methods.

eess.SY↗

arXiv2024

Learning with Dynamics: Autonomous Regulation of UAV Based Communication Networks with Dynamic UAV Crew

Unmanned Aerial Vehicle (UAV) based communication networks (UCNs) are a key component in future mobile networking. To handle the dynamic environments in UCNs, reinforcement learning (RL) has been a promising solution attributed to its strong capability of adaptive decision-making free of the environment models. However, most existing RL-based research focus on control strategy design assuming a fixed set of UAVs. Few works have investigated how UCNs should be adaptively regulated when the serving UAVs change dynamically. This article discusses RL-based strategy design for adaptive UCN regulation given a dynamic UAV set, addressing both reactive strategies in general UCNs and proactive strategies in solar-powered UCNs. An overview of the UCN and the RL framework is first provided. Potential research directions with key challenges and possible solutions are then elaborated. Some of our recent works are presented as case studies to inspire innovative ways to handle dynamic UAV crew with different RL algorithms.

eess.SY↗

arXiv2024

Learning PDEs from data on closed surfaces with sparse optimization

The discovery of underlying surface partial differential equation (PDE) from observational data has significant implications across various fields, bridging the gap between theory and observation, enhancing our understanding of complex systems, and providing valuable tools and insights for applications. In this paper, we propose a novel approach, termed physical-informed sparse optimization (PIS), for learning surface PDEs. Our approach incorporates both $L_2$ physical-informed model loss and $L_1$ regularization penalty terms in the loss function, enabling the identification of specific physical terms within the surface PDEs. The unknown function and the differential operators on surfaces are approximated by some extrinsic meshless methods. We provide practical demonstrations of the algorithms including linear and nonlinear systems. The numerical experiments on spheres and various other surfaces demonstrate the effectiveness of the proposed approach in simultaneously achieving precise solution prediction and identification of unknown PDEs.

math.NA↗

arXiv2024

When Learning Meets Dynamics: Distributed User Connectivity Maximization in UAV-Based Communication Networks

Distributed management over Unmanned Aerial Vehicle (UAV) based communication networks (UCNs) has attracted increasing research attention. In this work, we study a distributed user connectivity maximization problem in a UCN. The work features a horizontal study over different levels of information exchange during the distributed iteration and a consideration of dynamics in UAV set and user distribution, which are not well addressed in the existing works. Specifically, the studied problem is first formulated into a time-coupled mixed-integer non-convex optimization problem. A heuristic two-stage UAV-user association policy is proposed to faster determine the user connectivity. To tackle the NP-hard problem in scalable manner, the distributed user connectivity maximization algorithm 1 (DUCM-1) is proposed under the multi-agent deep Q learning (MA-DQL) framework. DUCM-1 emphasizes on designing different information exchange levels and evaluating how they impact the learning convergence with stationary and dynamic user distribution. To comply with the UAV dynamics, DUCM-2 algorithm is developed which is devoted to autonomously handling arbitrary quit's and join-in's of UAVs in a considered time horizon. Extensive simulations are conducted i) to conclude that exchanging state information with a deliberated task-specific reward function design yields the best convergence performance, and ii) to show the efficacy and robustness of DUCM-2 against the dynamics.

cs.NI↗

arXiv2024

LLM-based multi-agent poetry generation in non-cooperative environments

Despite substantial progress of large language models (LLMs) for automatic poetry generation, the generated poetry lacks diversity while the training process differs greatly from human learning. Under the rationale that the learning process of the poetry generation systems should be more human-like and their output more diverse and novel, we introduce a framework based on social learning where we emphasize non-cooperative interactions besides cooperative interactions to encourage diversity. Our experiments are the first attempt at LLM-based multi-agent systems in non-cooperative environments for poetry generation employing both TRAINING-BASED agents (GPT-2) and PROMPTING-BASED agents (GPT-3 and GPT-4). Our evaluation based on 96k generated poems shows that our framework benefits the poetry generation process for TRAINING-BASED agents resulting in 1) a 3.0-3.7 percentage point (pp) increase in diversity and a 5.6-11.3 pp increase in novelty according to distinct and novel n-grams. The generated poetry from TRAINING-BASED agents also exhibits group divergence in terms of lexicons, styles and semantics. PROMPTING-BASED agents in our framework also benefit from non-cooperative environments and a more diverse ensemble of models with non-homogeneous agents has the potential to further enhance diversity, with an increase of 7.0-17.5 pp according to our experiments. However, PROMPTING-BASED agents show a decrease in lexical diversity over time and do not exhibit the group-based divergence intended in the social network. Our paper argues for a paradigm shift in creative tasks such as automatic poetry generation to include social learning processes (via LLM-based agent modeling) similar to human interaction.

cs.CL↗

arXiv2024

BiGS: Bidirectional Gaussian Primitives for Relightable 3D Gaussian Splatting

We present Bidirectional Gaussian Primitives, an image-based novel view synthesis technique designed to represent and render 3D objects with surface and volumetric materials under dynamic illumination. Our approach integrates light intrinsic decomposition into the Gaussian splatting framework, enabling real-time relighting of 3D objects. To unify surface and volumetric material within a cohesive appearance model, we adopt a light- and view-dependent scattering representation via bidirectional spherical harmonics. Our model does not use a specific surface normal-related reflectance function, making it more compatible with volumetric representations like Gaussian splatting, where the normals are undefined. We demonstrate our method by reconstructing and rendering objects with complex materials. Using One-Light-At-a-Time (OLAT) data as input, we can reproduce photorealistic appearances under novel lighting conditions in real time.

cs.CV↗

arXiv2024

Convergent finite elements on arbitrary meshes, the WG method

On meshes with the maximum angle condition violated, the standard conforming, nonconforming, and discontinuous Galerkin finite elements do not converge to the true solution when the mesh size goes to zero. It is shown that one type of weak Galerkin finite element method converges on triangular and tetrahedral meshes violating the maximum angle condition, i.e., on arbitrary meshes. Numerical tests confirm the theory.

math.NA↗

arXiv2024

Cross-lingual Cross-temporal Summarization: Dataset, Models, Evaluation

While summarization has been extensively researched in natural language processing (NLP), cross-lingual cross-temporal summarization (CLCTS) is a largely unexplored area that has the potential to improve cross-cultural accessibility and understanding. This paper comprehensively addresses the CLCTS task, including dataset creation, modeling, and evaluation. We (1) build the first CLCTS corpus with 328 instances for hDe-En (extended version with 455 instances) and 289 for hEn-De (extended version with 501 instances), leveraging historical fiction texts and Wikipedia summaries in English and German; (2) examine the effectiveness of popular transformer end-to-end models with different intermediate finetuning tasks; (3) explore the potential of GPT-3.5 as a summarizer; (4) report evaluations from humans, GPT-4, and several recent automatic evaluation metrics. Our results indicate that intermediate task finetuned end-to-end models generate bad to moderate quality summaries while GPT-3.5, as a zero-shot summarizer, provides moderate to good quality outputs. GPT-3.5 also seems very adept at normalizing historical text. To assess data contamination in GPT-3.5, we design an adversarial attack scheme in which we find that GPT-3.5 performs slightly worse for unseen source documents compared to seen documents. Moreover, it sometimes hallucinates when the source sentences are inverted against its prior knowledge with a summarization accuracy of 0.67 for plot omission, 0.71 for entity swap, and 0.53 for plot negation. Overall, our regression results of model performances suggest that longer, older, and more complex source texts (all of which are more characteristic for historical language variants) are harder to summarize for all models, indicating the difficulty of the CLCTS task.

cs.CL↗

arXiv2024

Edge Intelligence Optimization for Large Language Model Inference with Batching and Quantization

Generative Artificial Intelligence (GAI) is taking the world by storm with its unparalleled content creation ability. Large Language Models (LLMs) are at the forefront of this movement. However, the significant resource demands of LLMs often require cloud hosting, which raises issues regarding privacy, latency, and usage limitations. Although edge intelligence has long been utilized to solve these challenges by enabling real-time AI computation on ubiquitous edge resources close to data sources, most research has focused on traditional AI models and has left a gap in addressing the unique characteristics of LLM inference, such as considerable model size, auto-regressive processes, and self-attention mechanisms. In this paper, we present an edge intelligence optimization problem tailored for LLM inference. Specifically, with the deployment of the batching technique and model quantization on resource-limited edge devices, we formulate an inference model for transformer decoder-based LLMs. Furthermore, our approach aims to maximize the inference throughput via batch scheduling and joint allocation of communication and computation resources, while also considering edge resource constraints and varying user requirements of latency and accuracy. To address this NP-hard problem, we develop an optimal Depth-First Tree-Searching algorithm with online tree-Pruning (DFTSP) that operates within a feasible time complexity. Simulation results indicate that DFTSP surpasses other batching benchmarks in throughput across diverse user settings and quantization techniques, and it reduces time complexity by over 45% compared to the brute-force searching method.

cs.LG↗

arXiv2024

The weak Galerkin finite element method for Stokes interface problems with curved interface

In this paper, we develop a new weak Galerkin finite element scheme for the Stokes interface problem with curved interfaces. We take a unique vector-valued function at the interface and reflect the interface condition in the variational problem. Theoretical analysis and numerical experiments show that the errors can reach the optimal convergence order under the energy norm and $L^2$ norm.

math.NA↗

arXiv2024

Helicity-conservative Physics-informed Neural Network Model for Navier-Stokes Equations

We design the helicity-conservative physics-informed neural network model for the Navier-Stokes equation in the ideal case. The key is to provide an appropriate PDE model as loss function so that its neural network solutions produce helicity conservation. Physics-informed neural network model is based on the strong form of PDE. We compare the proposed Physics-informed neural network model and a relevant helicity-conservative finite element method. We arrive at the conclusion that the strong form PDE is better suited for conservation issues. We also present theoretical justifications for helicity conservation as well as supporting numerical calculations.

physics.comp-ph↗