Publications (45)
Scaling Optimized Spectral Approximations on Unbounded Domains: The Generalized Hermite and Laguerre Methods
Hao Hu, Haijun Yu
We propose a novel error analysis framework for scaled generalized Laguerre and generalized Hermite approximations.This framework can be regarded as an analogue of the Nyquist-Shan…
Application of Bounded Total Variation Denoising in Urban Traffic Analysis
Shanshan Tang, Haijun Yu
While it is believed that denoising is not always necessary in many big data applications, we show in this paper that denoising is helpful in urban traffic analysis by applying the…
OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle
Haijun Yu, Xinyuan Tian, Weinan E +1
We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsage…
Fast Jacobi Spectral Methods and Closure Approximations for the Homogeneous FENE Model of Complex Fluids
Runkai Feng, Jie Shen, Haijun Yu
The Finitely Extensible Nonlinear Elastic (FENE) dumbbell model is a widely used mathematical model for complex fluids. Direct simulation of the FENE Fokker--Planck equation is com…
An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains
Yangyi Ye, Lin Li, Pengcheng Xie +1
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative prop…
On energy dissipation theory and numerical stability for time-fractional phase field equations
Tao Tang, Haijun Yu, Tao Zhou
For the time-fractional phase field models, the corresponding energy dissipation law has not been settled on both the continuous level and the discrete level. In this work, we shal…
Penalty-Free Natural Deep Ritz Method Based on de Rham Complex for High-Dimensional Dirichlet Boundary Value Problems
Jiarong Chen, Xia Ji, Haijun Yu +1
Deep neural networks show great promise for high-dimensional PDEs, yet enforcing essential boundary conditions remains challenging, especially as penalty parameters require problem…
OSNet & MNetO: Two Types of General Reconstruction Architectures for Linear Computed Tomography in Multi-Scenarios
Zhisheng Wang, Zihan Deng, Fenglin Liu +3
Recently, linear computed tomography (LCT) systems have actively attracted attention. To weaken projection truncation and image the region of interest (ROI) for LCT, the backprojec…
An Energy Stable Linear Diffusive Crank-Nicolson Scheme for the Cahn-Hilliard Gradient Flow
Lin Wang, Haijun Yu
We propose and analyze a linearly stabilized semi-implicit diffusive Crank--Nicolson scheme for the Cahn--Hilliard gradient flow. In this scheme, the nonlinear bulk force is treate…
Efficient Second Order Unconditionally Stable Schemes for a Phase-field Moving Contact Line Model Using Invariant Energy Quadratization Approach
Xiaofeng Yang, Haijun Yu
We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hi…
Constructing Custom Thermodynamics Using Deep Learning
Xiaoli Chen, Beatrice W. Soh, Zi-En Ooi +5
One of the most exciting applications of artificial intelligence (AI) is automated scientific discovery based on previously amassed data, coupled with restrictions provided by know…
A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation
Xinwei Hu, Jingrun Chen, Haijun Yu
The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical met…
Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence
Haijun Yu, Itzhak Fouxon, Jianchun Wang +4
We study Lyapunov exponents of tracers in compressible homogeneous isotropic turbulence at different turbulent Mach number and Taylor-scale Reynolds number . We demons…
An Efficient Stochastic Subgradient Method for the Global Placement Problem in Very Large-Scale Integration Circuits
Yi-Shuang Yue, Yu-Hong Dai, Haijun Yu
The placement problem in Very Large-Scale Integration (VLSI) circuits is a critical step in chip design. Its primary goal is to optimize the wirelength of circuit components within…
Convergence analysis of a finite element approximation of minimum action methods
Xiaoliang Wan, Haijun Yu, Jiayu Zhai
In this work, we address the convergence of a finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for non-gradient dynamical systems pert…
DLIMD: Dictionary Learning based Image-domain Material Decomposition for spectral CT
Weiwen Wu, Haijun Yu, Peijun Chen +7
The potential huge advantage of spectral computed tomography (CT) is its capability to provide accuracy material identification and quantitative tissue information. This can benefi…
An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
Shenghe Huang, Yishuang Yue, Haijun Yu
Minimum action methods provide a powerful framework for analyzing rare transitions in small-noise-driven dynamical systems, but their practical performance is often limited by time…
Spectral CT Reconstruction via Low-rank Representation and Structure Preserving Regularization
Yuanwei He, Li Zeng, Qiong Xu +5
With the development of computed tomography (CT) imaging technology, it is possible to acquire multi-energy data by spectral CT. Being different from conventional CT, the X-ray ene…
Predictive Moving Sample Method for Physics-Informed Neural Solvers of Time-Dependent PDEs
Beining Xu, Bocheng Zhang, Haijun Yu +2
Time-dependent partial differential equations (PDEs) often develop sharp fronts, localized peaks, and other moving structures that occupy only a small portion of the space--time do…
Convergence Analysis of an Unconditionally Energy Stable Linear Crank-Nicolson Scheme for the Cahn-Hilliard Equation
Lin Wang, Haijun Yu
Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analy…
On Efficient Second Order Stabilized Semi-Implicit Schemes for the Cahn-Hilliard Phase-Field Equation
Lin Wang, Haijun Yu
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and s…
Moving sample method for solving time-dependent partial differential equations
Beining Xu, Haijun Yu, Jiayu Zhai +2
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neura…
A kind of infinite-dimensional Novikov algebras and its realization
Liangyun Chen, Yao Ma, Haijun Yu
In this paper, we construct a kind of infinite-dimensional Novikov algebras and give its realization by hyperbolic sine functions and hyperbolic cosine functions.
Improved Laguerre Spectral Methods with Less Round-off Errors and Better Stability
Shenghe Huang, Haijun Yu
Laguerre polynomials are orthogonal polynomials defined on positive half line with respect to weight . They have wide applications in scientific and engineering computation…
ChebNet: Efficient and Stable Constructions of Deep Neural Networks with Rectified Power Units via Chebyshev Approximations
Shanshan Tang, Bo Li, Haijun Yu
In a previous study [B. Li, S. Tang and H. Yu, Commun. Comput. Phy. 27(2):379-411, 2020], it is shown that deep neural networks built with rectified power units (RePU) as activatio…
On the Influence of Smoothness Constraints in Computed Tomography Motion Compensation
Mareike Thies, Fabian Wagner, Noah Maul +6
Computed tomography (CT) relies on precise patient immobilization during image acquisition. Nevertheless, motion artifacts in the reconstructed images can persist. Motion compensat…
A Natural Deep Ritz Method for Essential Boundary Value Problems
Haijun Yu, Shuo Zhang
Deep neural network approaches show promise in solving partial differential equations. However, unlike traditional numerical methods, they face challenges in enforcing essential bo…
Energy Stable Second Order Linear Schemes for the Allen-Cahn Phase-Field Equation
Lin Wang, Haijun Yu
Phase-field model is a powerful mathematical tool to study the dynamics of interface and morphology changes in fluid mechanics and material sciences. However, numerically solving a…
BPF Algorithms for Multiple Source-Translation Computed Tomography Reconstruction
Zhisheng Wang, Haijun Yu, Yixing Huang +5
Micro-computed tomography (micro-CT) is a widely used state-of-the-art instrument employed to study the morphological structures of objects in various fields. However, its small fi…
Numerical Approximations for a Phase-Field Moving Contact Line Model with Variable Densities and Viscosities
Haijun Yu, Xiaofeng Yang
We consider the numerical approximations of a two-phase hydrodynamics coupled phase-field model that incorporates the variable densities, viscosities and moving contact line bounda…
Scaling Optimized Hermite Approximation Methods
Hao Hu, Haijun Yu
Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather t…
Improving Generalization of Deep Learning for Brain Metastases Segmentation Across Institutions
Yuchen Yang, Shuangyang Zhong, Haijun Yu +4
Background: Deep learning has demonstrated significant potential for automated brain metastases (BM) segmentation; however, models trained at a singular institution often exhibit s…
Structure-constrained Language-informed Diffusion Model for Unpaired Low-dose Computed Tomography Angiography Reconstruction
Genyuan Zhang, Zihao Wang, Zhifan Gao +10
The application of iodinated contrast media (ICM) improves the sensitivity and specificity of computed tomography (CT) for a wide range of clinical indications. However, overdose o…
Quantum CT via Dynamic Interval Encoding and Prior-Balanced QUBO Reconstruction
Ao Wang, Yikuang Yuluo, Yujie Liu +7
Quadratic unconstrained binary optimization (QUBO)-based quantum computed tomography (CT) casts reconstruction as a binary quadratic problem for quantum annealing and hybrid quantu…
A gradient-based approach to fast and accurate head motion compensation in cone-beam CT
Mareike Thies, Fabian Wagner, Noah Maul +9
Cone-beam computed tomography (CBCT) systems, with their flexibility, present a promising avenue for direct point-of-care medical imaging, particularly in critical scenarios such a…
PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power Units
Bo Li, Shanshan Tang, Haijun Yu
Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not con…
Quasi-potential Calculation and Minimum Action Method for Limit Cycle
Xiang Zhou, Haijun Yu, Ling Lin
We study the noise-induced escape from a stable limit cycle of a non-gradient dynamical system driven by a small additive noise. The fact that the optimal transition path in this c…
Efficient Image-to-Image Schrödinger Bridge for CT Field of View Extension
Zhenhao Li, Song Ni, Long Yang +6
Computed tomography (CT) is a cornerstone imaging modality for non-invasive, high-resolution visualization of internal anatomical structures. However, when the scanned object excee…
A Laguerre homotopy method for optimal control of nonlinear systems in semi-infinite interval
Haijun Yu, Hassan Saberi Nik
This paper presents a Laguerre homotopy method for optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-sc…
Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units
Bo Li, Shanshan Tang, Haijun Yu
Deep neural networks with rectified linear units (ReLU) are getting more and more popular due to their universal representation power and successful applications. Some theoretical…
Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines
Xianmin Xu, Yana Di, Haijun Yu
The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical…
Energetic Spectral-Element Time Marching Methods for Phase-Field Nonlinear Gradient Systems
Shiqin Liu, Haijun Yu
We propose two efficient energetic spectral-element methods in time for marching nonlinear gradient systems with the phase-field Allen--Cahn equation as an example: one fully impli…
Efficient Spectral Methods for Quasi-Equilibrium Closure Approximations of Symmetric Problems on Unit Circle and Sphere
Shan Jiang, Haijun Yu
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the…
Numerical approximation of elliptic problems with log-normal random coefficients
Xiaoliang Wan, Haijun Yu
In this work, we consider a non-standard preconditioning strategy for the numerical approximation of the classical elliptic equations with log-normal random coefficients. In \cite{…
Quantum Compressed Sensing CT Reconstruction Algorithm Based on Penalized Weighted Least Squares and Guided Total Variation
Yuwen Zhang, Yujie Liu, Ao Wang +4
Objective. Existing quadratic unconstrained binary optimization (QUBO)-based sparse-view computed tomography (CT) reconstruction neglects photon-counting statistics and anatomical…