Publications (49)
An Efficient High-order Numerical Solver for Diffusion Equations with Strong Anisotropy
David Green, Xiaozhe Hu, Jeremy Lore +2
In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for f…
Community Search in Time-dependent Road-social Attributed Networks
Li Ni, Hengkai Xu, Lin Mu +2
Real-world networks often involve both keywords and locations, along with travel time variations between locations due to traffic conditions. However, most existing cohesive subgra…
A Mesh-free Method Using Piecewise Deep Neural Network for Elliptic Interface Problems
Cuiyu He, Xiaozhe Hu, Lin Mu
In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks…
Robustness of Prompting: Enhancing Robustness of Large Language Models Against Prompting Attacks
Lin Mu, Guowei Chu, Li Ni +2
Large Language Models (LLMs) have demonstrated remarkable performance across various tasks by effectively utilizing a prompting strategy. However, they are highly sensitive to inpu…
A Weak Galerkin Finite Element Method for the Maxwell Equations
Lin Mu, Junping Wang, Xiu Ye +1
This paper introduces a numerical scheme for time harmonic Maxwell's equations by using weak Galerkin (WG) finite element methods. The WG finite element method is based on two oper…
From Clues to Generation: Language-Guided Conditional Diffusion for Cross-Domain Recommendation
Ziang Lu, Lei Sang, Lin Mu +1
Cross-domain Recommendation (CDR) exploits multi-domain correlations to alleviate data sparsity. As a core task within this field, inter-domain recommendation focuses on predicting…
Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening
Zixuan Cang, Lin Mu, Guowei Wei
This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the re…
A Discrete Divergence-Free Weak Galerkin Finite Element Method for the Stokes Equations
Lin Mu, Junping Wang, Xiu Ye
A discrete divergence-free weak Galerkin finite element method is developed for the Stokes equations based on a weak Galerkin (WG) method introduced in the reference [15]. Discrete…
GraphLoRA: Structure-Aware Low-Rank Adaptation for Large Language Model Recommendation
Lin Mu, Guoji Wang, Li Ni +4
Large Language Models (LLMs) have shown strong potential for recommendation (LLMRec) due to their powerful reasoning and generalization abilities. However, effectively aligning the…
Weak Galerkin Finite Element Methods for the Biharmonic Equation on Polytopal Meshes
Lin Mu, Junping Wang, Xiu Ye
A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for the biharmonic equation in its primary form. This method is highly robust and flexible i…
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation with Large Wave Numbers
Lin Mu, Junping Wang, Xiu Ye +1
Weak Galerkin (WG) refers to general finite element methods for partial differential equations in which differential operators are approximated by weak forms through the usual inte…
Fully discrete analysis of pressure-robust enriched Galerkin methods for the time-dependent Stokes equations
Seulip Lee, Lin Mu
This paper presents a fully discrete analysis of pressure-robust enriched Galerkin (EG) methods for the time-dependent Stokes equations. The spatial discretization employs a veloci…
Wave Climate from Spectra and its Connections with Local and Remote Wind Climate
Haoyu Jiang, Lin Mu
Because wind-generated waves can propagate over large distances, wave spectra from a fixed point can record information about air-sea interactions in distant areas. In this study,…
Pressure-robust enriched Galerkin finite element methods for coupled Navier-Stokes and heat equations
Sanjeeb Poudel, Sanghyun Lee, Lin Mu
We propose a pressure-robust enriched Galerkin (EG) finite element method for the incompressible Navier-Stokes and heat equations in the Boussinesq regime. For the Navier-Stokes eq…
A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations
Lin Mu, Junping Wang, Yanqiu Wang +1
The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye for general second order elliptic problems on triangular mes…
Pre-trained Prompt-driven Semi-supervised Local Community Detection
Li Ni, Hengkai Xu, Lin Mu +2
Semi-supervised local community detection aims to leverage known communities to detect the community containing a given node. Although existing semi-supervised local community dete…
A Domain-Decomposition Model Reduction Method for Linear Convection-Diffusion Equations with Random Coefficients
Lin Mu, Guannan Zhang
We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are…
L-UNet: An LSTM Network for Remote Sensing Image Change Detection
Shuting Sun, Lin Mu, Lizhe Wang +1
Change detection of high-resolution remote sensing images is an important task in earth observation and was extensively investigated. Recently, deep learning has shown to be very s…
A Hybridized Formulation for the Weak Galerkin Mixed Finite Element Method
Lin Mu, Junping Wang, Xiu Ye
This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed for second order elliptic equations. The…
A function space approach to the shape optimization of the Boussinesq system
Andrea Ceretani, Weiwei Hu, Lin Mu +1
We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a tempera…
A C^0-Weak Galerkin Finite Element Method for the Biharmonic Equation
Lin Mu, Junping Wang, Xiu Ye +1
A C^0-weak Galerkin (WG) method is introduced and analyzed for solving the biharmonic equation in 2D and 3D. A weak Laplacian is defined for C^0 functions in the new weak formulati…
Coloring for dispersion: A polynomial-time algorithm for cardinality-constrained 2-anticlustering
Nguyen Khoa Tran, Lin Mu, Martin Papenberg +1
The -Maximum Dispersion Problem with Cardinality Constraints (-MDCC) asks for a partition of a given item set with pairwise dissimilarities into cardinality-constrained g…
Weak Galerkin Methods for Second Order Elliptic Interface Problems
Lin Mu, Junping Wang, Guowei Wei +2
Weak Galerkin methods refer to general finite element methods for PDEs in which differential operators are approximated by their weak forms as distributions. Such weak forms give r…
Weakly Supervised Fine-grained Span-Level Framework for Chinese Radiology Report Quality Assurance
Kaiyu Wang, Lin Mu, Zhiyao Yang +3
Quality Assurance (QA) for radiology reports refers to judging whether the junior reports (written by junior doctors) are qualified. The QA scores of one junior report are given by…
Polynomial Expansion Rank Adaptation: Enhancing Low-Rank Fine-Tuning with High-Order Interactions
Wenhao Zhang, Lin Mu, Li Ni +2
Low-rank adaptation (LoRA) is a widely used strategy for efficient fine-tuning of large language models (LLMs), but its strictly linear structure fundamentally limits expressive ca…
TalkLoRA: Communication-Aware Mixture of Low-Rank Adaptation for Large Language Models
Lin Mu, Haiyang Wang, Li Ni +4
Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of Large Language Models (LLMs), and recent Mixture-of-Experts (MoE) extensions further enhance flexibility by dy…
Pressure-robust enriched Galerkin methods for the Stokes equations
Xiaozhe Hu, Seulip Lee, Lin Mu +1
In this paper, we present a pressure-robust enriched Galerkin (EG) scheme for solving the Stokes equations, which is an enhanced version of the EG scheme for the Stokes problem pro…
Tree-based Ensemble Learning for Out-of-distribution Detection
Zhaiming Shen, Menglun Wang, Guang Cheng +5
Being able to successfully determine whether the testing samples has similar distribution as the training samples is a fundamental question to address before we can safely deploy m…
From Representation to Clusters: A Contrastive Learning Approach for Attributed Hypergraph Clustering
Li Ni, Shuaikang Zeng, Lin Mu +1
Contrastive learning has demonstrated strong performance in attributed hypergraph clustering. Typically, existing methods based on contrastive learning first learn node embeddings…
A low-cost, parameter-free, and pressure-robust enriched Galerkin method for the Stokes equations
Seulip Lee, Lin Mu
In this paper, we propose a low-cost, parameter-free, and pressure-robust Stokes solver based on the enriched Galerkin (EG) method with a discontinuous velocity enrichment function…
A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations
Lin Mu, Junping Wang, Yanqiu Wang +1
This article introduces and analyzes a weak Galerkin mixed finite element method for solving the biharmonic equation. The weak Galerkin method, first introduced by two of the autho…
Effective Implementation of the Weak Galerkin Finite Element Methods for the Biharmonic Equation
Lin Mu, Junping Wang, Xiu Ye
The weak Galerkin (WG) methods have been introduced in the references [11, 16] for solving the biharmonic equation. The purpose of this paper is to develop an algorithm to implemen…
A topological approach for protein classification
Zixuan Cang, Lin Mu, Kedi Wu +3
Protein function and dynamics are closely related to its sequence and structure. However prediction of protein function and dynamics from its sequence and structure is still a fund…
Solving the linear transport equation by a deep neural network approach
Zheng Chen, Liu Liu, Lin Mu
In this paper, we study the linear transport model by adopting the deep learning method, in particular the deep neural network (DNN) approach. While the interest of using DNN to st…
Accelerating linear solvers for Stokes problems with C++ metaprogramming
Denis Demidov, Lin Mu, Bin Wang
The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increa…
Multiscale persistent functions for biomolecular structure characterization
Kelin Xia, Zhiming Li, Lin Mu
In this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions with per…
ComGPT: Detecting Local Community Structure with Large Language Models
Li Ni, Haowen Shen, Lin Mu +2
Large Language Models (LLMs), like GPT-3.5-turbo, have demonstrated the ability to understand graph structures and have achieved excellent performance in various graph reasoning ta…
Community and hyperedge inference in multiple hypergraphs
Li Ni, Ziqi Deng, Lin Mu +3
Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationshi…
A Pressure-Robust Weak Galerkin Finite Element Method for Navier-Stokes Equations
Lin Mu
In this paper, we develop and analyze a novel numerical scheme for the steady incompressible Navier-Stokes equations by the weak Galerkin methods. The divergence-preserving velocit…
An Immersed Weak Galerkin Method For Elliptic Interface Problems
Lin Mu, Xu Zhang
In this paper, we present an immersed weak Galerkin method for solving second-order elliptic interface problems. The proposed method does not require the meshes to be aligned with…
Optimal Control of Convection-Cooling and Numerical Implementation
Cuiyu He, Weiwei Hu, Lin Mu
This paper is concerned with the problem of enhancing convection-cooling via active control of the incompressible velocity field, described by a stationary diffusion-convection mod…
A uniform and pressure-robust enriched Galerkin method for the Brinkman equations
Seulip Lee, Lin Mu
This paper presents a pressure-robust enriched Galerkin (EG) method for the Brinkman equations with minimal degrees of freedom based on EG velocity and pressure spaces. The velocit…
A stabilizer free, pressure robust, and superconvergence weak Galerkin finite element method for the Stokes Equations on polytopal mesh
Lin Mu, Xiu Ye, Shangyou Zhang
In this paper, we propose a new stabilizer free and pressure robust WG method for the Stokes equations with super-convergence on polytopal mesh in the primary velocity-pressure for…
Weak Galerkin Finite Element Methods on Polytopal Meshes
Lin Mu, Junping Wang, Xiu Ye
This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a dis…
DenseLoRA: Dense Low-Rank Adaptation of Large Language Models
Lin Mu, Xiaoyu Wang, Li Ni +4
Low-rank adaptation (LoRA) has been developed as an efficient approach for adapting large language models (LLMs) by fine-tuning two low-rank matrices, thereby reducing the number o…
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation
Lin Mu, Junping Wang, Xiu Ye +1
A weak Galerkin (WG) method is introduced and numerically tested for the Helmholtz equation. This method is flexible by using discontinuous piecewise polynomials and retains the ma…
A Weak Galerkin Finite Element Method with Polynomial Reduction
Lin Mu, Junping Wang, Xiu Ye
The novel idea of weak Galerkin (WG) finite element methods is on the use of weak functions and their weak derivatives defined as distributions. Weak functions and weak derivatives…
A simple finite element method for the Stokes equations
Lin Mu, Xiu Ye
The goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation an…
A Stable Numerical Algorithm for the Brinkman Equations by Weak Galerkin Finite Element Methods
Lin Mu, Junping Wang, Xiu Ye
This paper presents a stable numerical algorithm for the Brinkman equations by using weak Galerkin (WG) finite element methods. The Brinkman equations can be viewed mathematically…