arXiv subjects

Yue Yu

Publications and source records attributed to Yue Yu.

At least 361 records · Page 20Linked to original sources

arXiv2022

On The Low Speed Limits of Lorentz's Transformation

This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the conventional language. We show that even under low speed limits, the relativistic effects should not be neglected to get a self-consistent theory of the electromagnetic fields, unless the intrinsic dynamics of these fields has been omitted completely. The quasi-static limits, where the relativistic effects can be partly neglected are also reviewed, to clarify some common misunderstandings and imprecise use of the theory in presence of moving media and other related situations. The discussion presented in this paper provide a clear view of why classical electromagnetic theory is relativistic in its essence.

physics.class-ph↗

arXiv2022

mVEM: A MATLAB Software Package for the Virtual Element Methods

This paper summarizes the development of mVEM, a MATLAB software package containing efficient and easy-following codes for various virtual element methods (VEMs) published in the literature. We explain in detail the numerical implementation of the mixed VEMs for the Darcy problem and the three-dimensional linear VEMs for the Poisson equation. For other model problems, we present the construction of the discrete methods and only provide the implementation of the elliptic projection matrices. Some mesh related functions are also given in the package, including the mesh generation and refinement in two or three dimensions. mVEM is free and open source software.

math.NA↗

arXiv2022

A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements

We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive model form nor possessing knowledges on the material microstructure. To this end, a material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve anterior leaflet, with which we build a neural operator learning model. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material microstructure properties learned implicitly from the data and naturally embedded in the network parameters. Using various combinations of loading protocols, we compare the predictivity of this framework with finite element analysis based on the phenomenological Fung-type model. From in-distribution tests, the predictivity of our approach presents good generalizability to different loading conditions and outperforms the conventional constitutive modeling at approximately one order of magnitude. When tested on out-of-distribution loading ratios, the neural operator learning approach becomes less effective. To improve the generalizability of our framework, we propose a physics-guided neural operator learning model via imposing partial physics knowledge. This method is shown to improve the model's extrapolative performance in the small-deformation regime. Our results demonstrate that with sufficient data coverage and/or guidance from partial physics constraints, the data-driven approach can be a more effective method for modeling biological materials than the traditional constitutive modeling.

cs.LG↗

arXiv2022

Universal topological quantum computation with strongly correlated Majorana edge modes

Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In Ref. \cite{hukane}, it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibobacci anyon $τ$ and a thermal operator anyon $\varepsilon$ in the tricritical Ising model. The deconfinement of $τ$ and $\varepsilon$ via the interaction between the fermion modes yields the anyon {collisions} and gives the braiding of either $τ$ or $\varepsilon$. With these braidings, the complete members {of} a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for 1-qubit as well as controlled-not gate for 2-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit {where the controlled-not gate turns out { to be} a probabilistic gate} and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor's integer factorization algorithm.

cond-mat.str-el↗

arXiv2022

PRBoost: Prompt-Based Rule Discovery and Boosting for Interactive Weakly-Supervised Learning

Weakly-supervised learning (WSL) has shown promising results in addressing label scarcity on many NLP tasks, but manually designing a comprehensive, high-quality labeling rule set is tedious and difficult. We study interactive weakly-supervised learning -- the problem of iteratively and automatically discovering novel labeling rules from data to improve the WSL model. Our proposed model, named PRBoost, achieves this goal via iterative prompt-based rule discovery and model boosting. It uses boosting to identify large-error instances and then discovers candidate rules from them by prompting pre-trained LMs with rule templates. The candidate rules are judged by human experts, and the accepted rules are used to generate complementary weak labels and strengthen the current model. Experiments on four tasks show PRBoost outperforms state-of-the-art WSL baselines up to 7.1% and bridges the gaps with fully supervised models. Our Implementation is available at \url{https://github.com/rz-zhang/PRBoost}.

cs.CL↗

arXiv2022

Bridging Pre-trained Models and Downstream Tasks for Source Code Understanding

With the great success of pre-trained models, the pretrain-then-finetune paradigm has been widely adopted on downstream tasks for source code understanding. However, compared to costly training a large-scale model from scratch, how to effectively adapt pre-trained models to a new task has not been fully explored. In this paper, we propose an approach to bridge pre-trained models and code-related tasks. We exploit semantic-preserving transformation to enrich downstream data diversity, and help pre-trained models learn semantic features invariant to these semantically equivalent transformations. Further, we introduce curriculum learning to organize the transformed data in an easy-to-hard manner to fine-tune existing pre-trained models. We apply our approach to a range of pre-trained models, and they significantly outperform the state-of-the-art models on tasks for source code understanding, such as algorithm classification, code clone detection, and code search. Our experiments even show that without heavy pre-training on code data, natural language pre-trained model RoBERTa fine-tuned with our lightweight approach could outperform or rival existing code pre-trained models fine-tuned on the above tasks, such as CodeBERT and GraphCodeBERT. This finding suggests that there is still much room for improvement in code pre-trained models.

cs.SE↗

arXiv2022

Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling

Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are present, these classical models may become inaccurate. In this work, we propose to use data-driven modeling, which directly utilizes high-fidelity simulation and/or experimental measurements to predict a material's response without using conventional constitutive models. Specifically, the material response is modeled by learning the implicit mappings between loading conditions and the resultant displacement and/or damage fields, with the neural network serving as a surrogate for a solution operator. To model the complex responses due to material heterogeneity and defects, we develop a novel deep neural operator architecture, which we coin as the Implicit Fourier Neural Operator (IFNO). In the IFNO, the increment between layers is modeled as an integral operator to capture the long-range dependencies in the feature space. As the network gets deeper, the limit of IFNO becomes a fixed point equation that yields an implicit neural operator and naturally mimics the displacement/damage fields solving procedure in material modeling problems. We demonstrate the performance of our proposed method for a number of examples, including hyperelastic, anisotropic and brittle materials. As an application, we further employ the proposed approach to learn the material models directly from digital image correlation (DIC) tracking measurements, and show that the learned solution operators substantially outperform the conventional constitutive models in predicting displacement fields.

cs.LG↗

arXiv2022

Smart Tracking Tray System for A Smart and Sustainable Wet Lab Community

The laboratories and research institutes are the major places for cutting-edge scientific exploration. Hundreds of millions of research papers were formed from front-line labs. Behind this glorious achievement were unsustainable facts. More and more human investment is required in innovative experimental design and analysis of results. However, the laboratory operating environment has not been subversively transformed for centuries. This abstract proposed a smart tracking system, consisting of IoT and Data Visualization technologies, to track the chemicals in an automatic and timely approach. Positive feedback has been collected from pilot tests in several labs. The system benefits various lab users in their daily work and improves their working efficiency. In the long run, it will play an essential role in promoting the efficient use of lab resources and achieving the goal of sustainable labs.

eess.SP↗

arXiv2022

Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's response. The solver with lower fidelity (coarse) is responsible for simulating domains with homogeneous features, whereas the expensive high-fidelity (fine) model describes microscopic features with refined discretization, often making the overall cost prohibitively high, especially for time-dependent problems. In this work, we explore the idea of multiscale modeling with machine learning and employ DeepONet, a neural operator, as an efficient surrogate of the expensive solver. DeepONet is trained offline using data acquired from the fine solver for learning the underlying and possibly unknown fine-scale dynamics. It is then coupled with standard PDE solvers for predicting the multiscale systems with new boundary/initial conditions in the coupling stage. The proposed framework significantly reduces the computational cost of multiscale simulations since the DeepONet inference cost is negligible, facilitating readily the incorporation of a plurality of interface conditions and coupling schemes. We present various benchmarks to assess accuracy and speedup, and in particular we develop a coupling algorithm for a time-dependent problem, and we also demonstrate coupling of a continuum model (finite element methods, FEM) with a neural operator representation of a particle system (Smoothed Particle Hydrodynamics, SPH) for a uniaxial tension problem with hyperelastic material. What makes this approach unique is that a well-trained over-parametrized DeepONet can generalize well and make predictions at a negligible cost.

cs.CE↗

arXiv2022

Programming of linear virtual element methods in three dimensions

We present a simple and efficient MATLAB implementation of the linear virtual element method for the three dimensional Poisson equation. The purpose of this software is primarily educational, to demonstrate how the key components of the method can be translated into code.

math.NA↗

arXiv2022

The Development and Prospect of Code Clone

The application of code clone technology accelerates code search, improves code reuse efficiency, and assists in software quality assessment and code vulnerability detection. However, the application of code clones also introduces software quality issues and increases the cost of software maintenance. As an important research field in software engineering, code clone has been extensively explored and studied by researchers, and related studies on various sub-research fields have emerged, including code clone detection, code clone evolution, code clone analysis, etc. However, there lacks a comprehensive exploration of the entire field of code clone, as well as an analysis of the trend of each sub-research field. This paper collects related work of code clones in the past ten years. In summary, the contributions of this paper mainly include: (1) summarize and classify the sub-research fields of code clone, and explore the relative popularity and relation of these sub-research fields; (2) analyze the overall research trend of code clone and each sub-research field; (3) compare and analyze the difference between academy and industry regarding code clone research; (4) construct a network of researchers, and excavate the major contributors in code clone research field; (5) The list of popular conferences and journals was statistically analyzed. The popular research directions in the future include clone visualization, clone management, etc. For the clone detection technique, researchers can optimize the scalability and execution efficiency of the method, targeting particular clone detection tasks and contextual environments, or apply the technology to other related research fields continuously.

cs.SE↗

arXiv2022

A Survey on Programmatic Weak Supervision

Labeling training data has become one of the major roadblocks to using machine learning. Among various weak supervision paradigms, programmatic weak supervision (PWS) has achieved remarkable success in easing the manual labeling bottleneck by programmatically synthesizing training labels from multiple potentially noisy supervision sources. This paper presents a comprehensive survey of recent advances in PWS. In particular, we give a brief introduction of the PWS learning paradigm, and review representative approaches for each component within PWS's learning workflow. In addition, we discuss complementary learning paradigms for tackling limited labeled data scenarios and how these related approaches can be used in conjunction with PWS. Finally, we identify several critical challenges that remain under-explored in the area to hopefully inspire future research directions in the field.

cs.LG↗

arXiv2022

A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials

In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in material microstructures, and to provide statistic metrics for quantities of interest, such as the fracture toughness. To depict the material responses and naturally describe the nucleation and growth of fractures, we consider the peridynamics model. In particular, a stochastic state-based peridynamic model is developed, where the micromechanical parameters are modeled by a finite-dimensional random vector, or a combination of random variables truncating the Karhunen-Loève decomposition or the principle component analysis (PCA). To solve this stochastic peridynamic problem, probabilistic collocation method (PCM) is employed to sample the random field representing the micromechanical parameters. For each sample, the deterministic peridynamic problem is discretized with an optimization-based meshfree quadrature rule. We present rigorous analysis for the proposed scheme and demonstrate its convergence for a number of benchmark problems, showing that it sustains the asymptotic compatibility spatially and achieves an algebraic or sub-exponential convergence rate in the random space as the number of collocation points grows. Finally, to validate the applicability of this approach on real-world fracture problems, we consider the problem of crystallization toughening in glass-ceramic materials, in which the material at the microstructural scale contains both amorphous glass and crystalline phases. The proposed stochastic peridynamic solver is employed to capture the crack initiation and growth for glass-ceramics with different crystal volume fractions, and the averaged fracture toughness are calculated. The numerical estimates of fracture toughness show good consistency with experimental measurements.

cond-mat.mtrl-sci↗

arXiv2022

A novel locking-free virtual element method for linear elasticity problems

This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one $\widetilde{K}$ with additional vertices consisting of interior points on edges of $K$, so that the discrete admissible space is taken as the $V_1$ type virtual element space related to the partition $\{\widetilde{K}\}$ instead of $\{K\}$. The method is shown to be uniformly convergent with the optimal rates both in $H^1$ and $L^2$ norms with respect to the Lamé constant $λ$. Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.

math.NA↗

arXiv2022

Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN's optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.

cs.LG↗

arXiv2022

A sparse grid discrete ordinate discontinuous Galerkin method for the radiative transfer equation

The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this bottleneck, we first use the discrete ordinate technique to discretize the scattering term, an integral with respect to the angular variables, resulting in a semi-discrete hyperbolic system. Then, we make the spatial discretization by means of the discontinuous Galerkin (DG) method combined with the sparse grid method. The final linear system is solved by the block Gauss-Seidal iteration method. The computational complexity and error analysis are developed in detail, which show the new method is more efficient than the original discrete ordinate DG method. A series of numerical results are performed to validate the convergence behavior and effectiveness of the proposed method.

math.NA↗

arXiv2021

A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for linear elasticity problems

We develop a lowest-order nonconforming virtual element method for planar linear elasticity, which can be viewed as an extension of the idea in Falk (1991) to the virtual element method (VEM), with the family of polygonal meshes satisfying a very general geometric assumption. The method is shown to be uniformly convergent for the nearly incompressible case with optimal rates of convergence. The crucial step is to establish the discrete Korn's inequality, yielding the coercivity of the discrete bilinear form. We also provide a unified locking-free scheme both for the conforming and nonconforming VEMs in the lowest order case. Numerical results validate the feasibility and effectiveness of the proposed numerical algorithms.

math.NA↗

arXiv2021

NeuronFair: Interpretable White-Box Fairness Testing through Biased Neuron Identification

Deep neural networks (DNNs) have demonstrated their outperformance in various domains. However, it raises a social concern whether DNNs can produce reliable and fair decisions especially when they are applied to sensitive domains involving valuable resource allocation, such as education, loan, and employment. It is crucial to conduct fairness testing before DNNs are reliably deployed to such sensitive domains, i.e., generating as many instances as possible to uncover fairness violations. However, the existing testing methods are still limited from three aspects: interpretability, performance, and generalizability. To overcome the challenges, we propose NeuronFair, a new DNN fairness testing framework that differs from previous work in several key aspects: (1) interpretable - it quantitatively interprets DNNs' fairness violations for the biased decision; (2) effective - it uses the interpretation results to guide the generation of more diverse instances in less time; (3) generic - it can handle both structured and unstructured data. Extensive evaluations across 7 datasets and the corresponding DNNs demonstrate NeuronFair's superior performance. For instance, on structured datasets, it generates much more instances (~x5.84) and saves more time (with an average speedup of 534.56%) compared with the state-of-the-art methods. Besides, the instances of NeuronFair can also be leveraged to improve the fairness of the biased DNNs, which helps build more fair and trustworthy deep learning systems.

cs.LG↗