arXiv subjects

Yingjie Liu

Publications and source records attributed to Yingjie Liu.

35 records · Page 2Linked to original sources

arXiv2022

A ghost-point based second order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering around PEC

We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor that impedes the propagations of electromagnetic waves. Our method is a modification of the existing approach by Zou and Liu [36], from a locally perturbed body-fitted grid to a uniform orthogonal one for complicated PEC objects. Similar to their work we extrapolate ghost point values by exploiting the level set function of the interface and the PDE-based extension technique, which allows us to circumvent scrutinizing local geometries of the interface. We stipulate a mild requirement on the accuracy of our extrapolation that the ghost values need only be locally second order accurate. Nevertheless the resulting accuracy of our method is second order thanks to the application of back and forth error correction and compensation, which also relaxes CFL conditions. We demonstrate the effectiveness of our approach with some numerical examples.

math.NA↗

arXiv2022

Numerical Identification of Nonlocal Potential in Aggregation

Aggregation equations are broadly used to model population dynamics with nonlocal interactions, characterized by a potential in the equation. This paper considers the inverse problem of identifying the potential from a single noisy spatial-temporal process. The identification is challenging in the presence of noise due to the instability of numerical differentiation. We propose a robust model-based technique to identify the potential by minimizing a regularized data fidelity term, and regularization is taken as the total variation and the squared Laplacian. A split Bregman method is used to solve the regularized optimization problem. Our method is robust to noise by utilizing a Successively Denoised Differentiation technique. We consider additional constraints such as compact support and symmetry constraints to enhance the performance further. We also apply this method to identify time-varying potentials and identify the interaction kernel in an agent-based system. Various numerical examples in one and two dimensions are included to verify the effectiveness and robustness of the proposed method.

math.NA↗

arXiv2022

Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems

In our prior work [arXiv:2109.09316], neural network methods with inputs based on domain of dependence and a converging sequence were introduced for solving one dimensional conservation laws, in particular the Euler systems. To predict a high-fidelity solution at a given space-time location, two solutions of a conservation law from a converging sequence, computed from low-cost numerical schemes, and in a local domain of dependence of the space-time location, serve as the input of a neural network. In the present work, we extend the methods to two dimensional Euler systems and introduce variations. Numerical results demonstrate that the methods not only work very well in one dimension [arXiv:2109.09316], but also perform well in two dimensions. Despite smeared local input data, the neural network methods are able to predict shocks, contacts, and smooth regions of the solution accurately. The neural network methods are efficient and relatively easy to train because they are local solvers.

math.NA↗

arXiv2022

O-ViT: Orthogonal Vision Transformer

Inspired by the tremendous success of the self-attention mechanism in natural language processing, the Vision Transformer (ViT) creatively applies it to image patch sequences and achieves incredible performance. However, the scaled dot-product self-attention of ViT brings about scale ambiguity to the structure of the original feature space. To address this problem, we propose a novel method named Orthogonal Vision Transformer (O-ViT), to optimize ViT from the geometric perspective. O-ViT limits parameters of self-attention blocks to be on the norm-keeping orthogonal manifold, which can keep the geometry of the feature space. Moreover, O-ViT achieves both orthogonal constraints and cheap optimization overhead by adopting a surjective mapping between the orthogonal group and its Lie algebra.We have conducted comparative experiments on image recognition tasks to demonstrate O-ViT's validity and experiments show that O-ViT can boost the performance of ViT by up to 3.6%.

cs.CV↗

arXiv2022

SparGE: Sparse Coding-based Patient Similarity Learning via Low-rank Constraints and Graph Embedding

Patient similarity assessment (PSA) is pivotal to evidence-based and personalized medicine, enabled by analyzing the increasingly available electronic health records (EHRs). However, machine learning approaches for PSA has to deal with inherent data deficiencies of EHRs, namely missing values, noise, and small sample sizes. In this work, an end-to-end discriminative learning framework, called SparGE, is proposed to address these data challenges of EHR for PSA. SparGE measures similarity by jointly sparse coding and graph embedding. First, we use low-rank constrained sparse coding to identify and calculate weight for similar patients, while denoising against missing values. Then, graph embedding on sparse representations is adopted to measure the similarity between patient pairs via preserving local relationships defined by distances. Finally, a global cost function is constructed to optimize related parameters. Experimental results on two private and public real-world healthcare datasets, namely SingHEART and MIMIC-III, show that the proposed SparGE significantly outperforms other machine learning patient similarity methods.

cs.LG↗

arXiv2021

Accuracy Enhancing Interface Treatment Algorithm: the Back and Forth Error Compensation and Correction method

The accuracy of information transmission while solving domain decomposed problems is crucial to smooth transition of a solution around the interface/overlapping region. This paper describes a systematical study on an accuracy enhancing interface treatment algorithm based on the back and forth error compensation and correction method (BFECC). By repetitively employing a low order interpolation technique (normally local 2\ts{nd} order) 3 times, this algorithm achieves local 3\ts{rd} order accuracy. Analytical derivations for 1D \& 2D cases are made, and the "super convergence" phenomenon (4\ts{th} order accuracy) is found for specific positioning of the donor and target grids. A set of numerical experiments based on various relative displacements, relative rotations, mesh ratios, and meshes with perturbation have been tested, and the results match the derivations. Different interface treatments are compared with 3D examples: corner flow and cavity flow. The component convergence rate analysis shows that the BFECC method positively affects the accuracy of solutions.

math.NA↗

arXiv2021

Room temperature energy-efficient spin-orbit torque switching in wafer-scale all-vdW heterostructure

The emergent two-dimensional (2D) ferromagnetic materials with unique magnetic properties have endowed great potential for next-generation spintronic devices with extraordinary merits of high flexibility, easy controllability, and high heretointegrability, which is expected to promote the development of Moore's Law continuously. However, it is extremely challenging to realize magnetic switching with ultra-low power consumption at room temperature. Here, we demonstrate the room-temperature spin-orbit torque (SOT) driven magnetization switching in a well-epitaxial all-van der Waals (vdW) heterostructure. The topological insulator Bi2Te3 not only helps to elevate the Curie temperature of Fe3GeTe2 (FGT) through interfacial exchange coupling but also works as a spin current source allowing to switch FGT at a low current density of 2.2 * 106 A cm2. A large SOT efficiency of 0.7 is measured at room temperature, and the thickness of FGT is further adjusted to reduce the influence of the thermal contribution on the second-harmonic signal. Furthermore, the temperature and thickness-dependent SOT efficiency prove that the large SOT in our system mainly originates from the nontrivial origin of topological materials. Our experiment has enabled an all-vdW SOT structure and lays a solid foundation for the implementation of room-temperature all-vdW spintronic devices in the future.

physics.app-ph↗

arXiv2021

Neural Networks with Inputs Based on Domain of Dependence and A Converging Sequence for Solving Conservation Laws, Part I: 1D Riemann Problems

Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear problems, e.g. the Burger's equation, heat conduction equations, Allen-Cahn and other reaction-diffusion equations, and Navier-Stokes equation. Meanwhile, researchers apply automatic differentiation in physics-informed neural network (PINN) to solve nonlinear hyperbolic systems based on conservation laws with highly discontinuous transition, such as Riemann problem, by inverse problem formulation in data-driven approach. However, it remains a challenge for forward methods using DNNs without knowing part of the solution to resolve discontinuities in nonlinear conservation laws. In this study, we incorporate 1st order numerical schemes into DNNs to set up the loss functional approximator instead of auto-differentiation from traditional deep learning framework, e.g. TensorFlow package, which improves the effectiveness of capturing discontinuities in Riemann problems. In particular, the 2-Coarse-Grid neural network (2CGNN) and 2-Diffusion-Coefficient neural network (2DCNN) are introduced in this work. We use 2 solutions of a conservation law from a converging sequence, computed from a low-cost numerical scheme, and in a domain of dependence of a space-time grid point as the input for a neural network to predict its high-fidelity solution at the grid point. Despite smeared input solutions, they output sharp approximations to solutions containing shocks and contacts and are efficient to use once trained.

math.NA↗

arXiv2021

A Finite Difference Method on Irregular Grids with Local Second Order Ghost Point Extension for Solving Maxwell's Equations Around Curved PEC Objects

A new finite difference method on irregular, locally perturbed rectangular grids has been developed for solving electromagnetic waves around curved perfect electric conductors (PEC). This method incorporates the back and forth error compensation and correction method (BFECC) and level set method to achieve convenience and higher order of accuracy at complicated PEC boundaries. A PDE-based local second order ghost cell extension technique is developed based on the level set framework in order to compute the boundary value to first order accuracy (cumulatively), and then BFECC is applied to further improve the accuracy while increasing the CFL number. Numerical experiments are conducted to validate the properties of the method.

math.NA↗

arXiv2020

Dense Multiscale Feature Fusion Pyramid Networks for Object Detection in UAV-Captured Images

Although much significant progress has been made in the research field of object detection with deep learning, there still exists a challenging task for the objects with small size, which is notably pronounced in UAV-captured images. Addressing these issues, it is a critical need to explore the feature extraction methods that can extract more sufficient feature information of small objects. In this paper, we propose a novel method called Dense Multiscale Feature Fusion Pyramid Networks(DMFFPN), which is aimed at obtaining rich features as much as possible, improving the information propagation and reuse. Specifically, the dense connection is designed to fully utilize the representation from the different convolutional layers. Furthermore, cascade architecture is applied in the second stage to enhance the localization capability. Experiments on the drone-based datasets named VisDrone-DET suggest a competitive performance of our method.

cs.CV↗

arXiv2019

IDENT: Identifying Differential Equations with Numerical Time evolution

Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying coefficients add complexity to the problem. We assume that the governing partial differential equation (PDE) is a linear combination of a subset of a prescribed dictionary containing different differential terms, and the objective of this paper is to find the correct coefficients. We propose a new direction based on the fundamental idea of convergence analysis of numerical PDE schemes. We utilize Lasso for efficiency, and a performance guarantee is established based on an incoherence property. The main contribution is to validate and correct the results by Time Evolution Error (TEE). The new algorithm, called Identifying Differential Equations with Numerical Time evolution (IDENT), is explored for data with non-periodic boundary conditions, noisy data and PDEs with varying coefficients. From the recovery analysis of Lasso, we propose a new definition of Noise-to-Signal ratio, which better represents the level of noise in the case of PDE identification. We systematically analyze the effects of data generations and downsampling, and propose an order preserving denoising method called Least-Squares Moving Average (LSMA), to preprocess the given data. For the identification of PDEs with varying coefficients, we propose to add Base Element Expansion (BEE) to aide the computation. Various numerical experiments from basic tests to noisy data, downsampling effects and varying coefficients are presented.

math.NA↗

arXiv2018

Arbitrarily routed mode-division multiplexed photonic circuits for dense integration

Mode-division multiplexing (MDM) is becoming an enabling technique for large-capacity data communications via encoding the information on orthogonal guiding modes. However, the on-chip routing of a multimode waveguide occupies too large chip area due to the constraints on inter-mode cross talk and mode leakage. Very recently, many efforts have been made to shrink the footprint of individual element like bending and crossing, but the devices still occupy >10x10 um2 footprint for three-mode multiplexed signals and the high-speed signal transmission has not been demonstrated yet. In this work, we demonstrate the first MDM circuits based on digitized meta-structures which have extremely compact footprints. The radius for a three-mode bending is only 3.9 μm and the footprint of a crossing is only 8x8um2. The 3x100 Gbit/s mode-multiplexed signals are arbitrarily routed through the circuits consists of many sharp bends and compact crossing with a bit error rate under forward error correction limit. This work is a significant step towards the large-scale and dense integration of MDM photonic integrated circuits.

physics.app-ph↗

arXiv2018

A phase-field formulation for dynamic cohesive fracture

We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress-strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro- and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation, with particular emphasis on dynamic fracture.

physics.app-ph↗

arXiv2018

Back and Forth Error Compensation and Correction Method for Linear Hyperbolic Systems with Application to the Maxwell's equations

We study the Back and Forth Error Compensation and Correction (BFECC) method for linear hyperbolic PDE systems. The BFECC method has been applied to schemes for advection equations to improve their stability and order of accuracy. Similar results are established in this paper for schemes for linear hyperbolic PDE systems with constant coefficients. We apply the BFECC method to central difference scheme and Lax-Friedrichs scheme for the Maxwell's equations and obtain second order accurate schemes with larger CFL number than the classical Yee scheme. The method is further applied to schemes on non-orthogonal unstructured grids. The new BFECC schemes for the Maxwell's equations operate on a single non-staggered grid and are simple to implement on unstructured grids. Numerical examples are given to demonstrate the effectiveness of the new schemes.

math.NA↗

arXiv2017

A Methodology for Projection-Based Model Reduction with Black-Box High-Fidelity Models

This paper presents a methodology that enables projection-based model reduction for black-box high-fidelity models such as commercial CFD codes. The methodology specifically addresses the situation where the high-fidelity model may be a black-box but there is complete knowledge of the governing equations. The main idea is that the linear operator matrix, resulting from the discretization of the linear differential terms is approximated directly using a suitable discretization method such as the Finite Volume Method and requires only the computational grid as input. In this regard, the governing equations are first cast in terms of a set of scalar observables of the state variables, leading to a linear set of equations. By applying the snapshots of the observables to the discrete linear operator, a right hand side vector is obtained, providing the necessary system matrices for the Galerkin projection step. This way an online database of ROMs are generated for various parameter snapshots which are then interpolated online to predict the state for new parameter instances. Finally, the reduced order model is posed as a non-linear constrained optimization problem that can be solved at a significantly cheaper cost compared to the full order model. The method is successfully demonstrated on on a canonical non-linear parametric PDE with exponential non-linearity, followed by the compressible inviscid ow past the NACA0012 airfoil. As a first step, this paper focuses only on establishing feasibility of the method.

math.AP↗

arXiv2017

Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers

A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer as the surfactant concentration increases through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. The importance of surface tension differences is quantified by means of a dimensionless parameter, revealing thresholds that separate different regimes of fracture. These findings are supported by newly performed experiments that validate the model and demonstrate the strong sensitivity of the fracture pattern to differences in surface tension.

cond-mat.soft↗

arXiv2014

Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System

We develop well-balanced central schemes on overlapping cells for the Saint-Venant shallow water system and its variants. The main challenge in deriving the schemes is related to the fact that the Saint-Venant system contains a geometric source term due to nonflat bottom topography and therefore a delicate balance between the flux gradients and source terms has to be preserved. We propose a constant subtraction technique, which helps one to ensure a well-balanced property of the schemes, while maintaining arbitrary high-order of accuracy. Hierarchical reconstruction limiting procedure is applied to eliminate spurious oscillations without using characteristic decomposition. Extensive one- and two-dimensional numerical simulations are conducted to verify the well-balanced property, high-order of accuracy, and non-oscillatory high-resolution for both smooth and nonsmooth solutions.

math.NA↗