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Dan Li

Publications and source records attributed to Dan Li.

At least 145 records · Page 8Linked to original sources

Faster Ray Tracing through Hierarchy Cut Code

We propose a novel ray reordering technique to accelerate the ray tracing process by encoding and sorting rays prior to traversal. Instead of spatial coordinates, our method encodes rays according to the cuts of the hierarchical acceleration structure, which is called the hierarchy cut code. This approach can better adapt to the acceleration structure and obtain a more reliable encoding result. We also propose a compression scheme to decrease the sorting overhead by a shorter sorting key. In addition, based on the phenomenon of boundary drift, we theoretically explain the reason why existing reordering methods cannot achieve better performance by using longer sorting keys. The experiment demonstrates that our method can accelerate secondary ray tracing by up to 1.81 times, outperforming the existing methods. Such result proves the effectiveness of hierarchy cut code, and indicate that the reordering technique can achieve greater performance improvement, which worth further research.

cs.GR↗

An Extension of the Morley Element on General Polytopal Partitions Using Weak Galerkin Methods

This paper introduces an extension of the well-known Morley element for the biharmonic equation, extending its application from triangular elements to general polytopal elements using the weak Galerkin finite element methods. By leveraging the Schur complement of the weak Galerkin method, this extension not only preserves the same degrees of freedom as the Morley element on triangular elements but also expands its applicability to general polytopal elements. The numerical scheme is devised by locally constructing weak tangential derivatives and weak second-order partial derivatives. Error estimates for the numerical approximation are established in both the energy norm and the $L^2$ norm. A series of numerical experiments are conducted to validate the theoretical developments.

math.NA↗

High Order Morley Elements for Biharmonic Equations on Polytopal Partitions

This paper introduces an extension of the Morley element for approximating solutions to biharmonic equations. Traditionally limited to piecewise quadratic polynomials on triangular elements, the extension leverages weak Galerkin finite element methods to accommodate higher degrees of polynomials and the flexibility of general polytopal elements. By utilizing the Schur complement of the weak Galerkin method, the extension allows for fewest local degrees of freedom while maintaining sufficient accuracy and stability for the numerical solutions. The numerical scheme incorporates locally constructed weak tangential derivatives and weak second order partial derivatives, resulting in an accurate approximation of the biharmonic equation. Optimal order error estimates in both a discrete $H^2$ norm and the usual $L^2$ norm are established to assess the accuracy of the numerical approximation. Additionally, numerical results are presented to validate the developed theory and demonstrate the effectiveness of the proposed extension.

math.NA↗

Generalized weak Galerkin finite element methods for second order elliptic problems

This article proposes and analyzes the generalized weak Galerkin ({\rm g}WG) finite element method for the second order elliptic problem. A generalized discrete weak gradient operator is introduced in the weak Galerkin framework so that the {\rm g}WG methods would not only allow arbitrary combinations of piecewise polynomials defined in the interior and on the boundary of each local finite element, but also work on general polytopal partitions. Error estimates are established for the corresponding numerical functions in the energy norm and the usual $L^2$ norm. A series of numerical experiments are presented to demonstrate the performance of the newly proposed {\rm g}WG method.

math.NA↗

GLHAD: A Group Lasso-based Hybrid Attack Detection and Localization Framework for Multistage Manufacturing Systems

As Industry 4.0 and digitalization continue to advance, the reliance on information technology increases, making the world more vulnerable to cyber-attacks, especially cyber-physical attacks that can manipulate physical systems and compromise operational data integrity. Detecting cyber-attacks in multistage manufacturing systems (MMS) is crucial due to the growing sophistication of attacks and the complexity of MMS. Attacks can propagate throughout the system, affecting subsequent stages and making detection more challenging than in single-stage systems. Localization is also critical due to the complex interactions in MMS. To address these challenges, a group lasso regression-based framework is proposed to detect and localize attacks in MMS. The proposed algorithm outperforms traditional hypothesis testing-based methods in expected detection delay and localization accuracy, as demonstrated in a linear multistage manufacturing system.

stat.AP↗

Missingness Augmentation: A General Approach for Improving Generative Imputation Models

Missing data imputation is a fundamental problem in data analysis, and many studies have been conducted to improve its performance by exploring model structures and learning procedures. However, data augmentation, as a simple yet effective method, has not received enough attention in this area. In this paper, we propose a novel data augmentation method called Missingness Augmentation (MisA) for generative imputation models. Our approach dynamically produces incomplete samples at each epoch by utilizing the generator's output, constraining the augmented samples using a simple reconstruction loss, and combining this loss with the original loss to form the final optimization objective. As a general augmentation technique, MisA can be easily integrated into generative imputation frameworks, providing a simple yet effective way to enhance their performance. Experimental results demonstrate that MisA significantly improves the performance of many recently proposed generative imputation models on a variety of tabular and image datasets. The code is available at \url{https://github.com/WYu-Feng/Missingness-Augmentation}.

cs.LG↗

A high-fidelity quantum state transfer algorithm on the complete bipartite graph

High-fidelity quantum state transfer is critical for quantum communication and scalable quantum computation. Current quantum state transfer algorithms on the complete bipartite graph, which are based on discrete-time quantum walk search algorithms, suffer from low fidelity in some cases. To solve this problem, in this paper we propose a two-stage quantum state transfer algorithm on the complete bipartite graph. The algorithm is achieved by the generalized Grover walk with one marked vertex. The generalized Grover walk's coin operators and the query oracles are both parametric unitary matrices, which are designed flexibly based on the positions of the sender and receiver and the size of the complete bipartite graph. We prove that the fidelity of the algorithm is greater than $1-2ε_{1}-ε_{2}-2\sqrt{2}\sqrt{ε_{1}ε_{2}}$ or $1-(2+2\sqrt{2})ε_{1}-ε_{2}-(2+2\sqrt{2})\sqrt{ε_{1}ε_{2}}$ for any adjustable parameters $ε_{1}$ and $ε_{2}$ when the sender and receiver are in the same partition or different partitions of the complete bipartite graph. The algorithm provides a novel approach to achieve high-fidelity quantum state transfer on the complete bipartite graph in any case, which will offer potential applications for quantum information processing.

quant-ph↗

Generalized Weak Galerkin Finite Element Methods for Biharmonic Equations

The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new generalized discrete weak second order partial derivative is introduced in the gWG scheme to allow arbitrary combinations of piecewise polynomial functions defined in the interior and on the boundary of general polygonal or polyhedral elements. The error estimates are established for the numerical approximation in a discrete H^2 norm and a L^2 norm. The numerical results are reported to demonstrate the accuracy and flexibility of our proposed gWG method for the biharmonic equation.

math.NA↗

An $L^p$-primal-dual finite element method for first-order transport problems

A new $L^p$-primal-dual weak Galerkin method ($L^p$-PDWG) with $p>1$ is proposed for the first-order transport problems. The existence and uniqueness of the $L^p$-PDWG numerical solutions is established. In addition, the $L^p$-PDWG method offers a numerical solution which retains mass conservation locally on each element. An optimal order error estimate is established for the primal variable. A series of numerical results are presented to verify the efficiency and accuracy of the proposed $L^p$-PDWG scheme.

math.NA↗

Decentral and Incentivized Federated Learning Frameworks: A Systematic Literature Review

The advent of Federated Learning (FL) has ignited a new paradigm for parallel and confidential decentralized Machine Learning (ML) with the potential of utilizing the computational power of a vast number of IoT, mobile and edge devices without data leaving the respective device, ensuring privacy by design. Yet, in order to scale this new paradigm beyond small groups of already entrusted entities towards mass adoption, the Federated Learning Framework (FLF) has to become (i) truly decentralized and (ii) participants have to be incentivized. This is the first systematic literature review analyzing holistic FLFs in the domain of both, decentralized and incentivized federated learning. 422 publications were retrieved, by querying 12 major scientific databases. Finally, 40 articles remained after a systematic review and filtering process for in-depth examination. Although having massive potential to direct the future of a more distributed and secure AI, none of the analyzed FLF is production-ready. The approaches vary heavily in terms of use-cases, system design, solved issues and thoroughness. We are the first to provide a systematic approach to classify and quantify differences between FLF, exposing limitations of current works and derive future directions for research in this novel domain.

cs.LG↗

Curved Elements in Weak Galerkin Finite Element Methods

A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on the boundary of the whole domain in two dimensions. The optimal orders of error estimates for the weak Galerkin approximations in both the $H^1$-norm and the $L^2$-norm are established. Numerical results are reported to demonstrate the performance of the weak Galerkin methods on general curved polygonal partitions.

math.NA↗

VIRT: Improving Representation-based Models for Text Matching through Virtual Interaction

With the booming of pre-trained transformers, representation-based models based on Siamese transformer encoders have become mainstream techniques for efficient text matching. However, these models suffer from severe performance degradation due to the lack of interaction between the text pair, compared with interaction-based models. Prior arts attempt to address this through performing extra interaction for Siamese encoded representations, while the interaction during encoding is still ignored. To remedy this, we propose a \textit{Virtual} InteRacTion mechanism (VIRT) to transfer interactive knowledge from interaction-based models into Siamese encoders through attention map distillation. As a train-time-only component, VIRT could completely maintain the high efficiency of the Siamese structure and brings no extra computation cost during inference. To fully utilize the learned interactive knowledge, we further design a VIRT-adapted interaction strategy. Experimental results on multiple text matching datasets demonstrate that our method outperforms state-of-the-art representation-based models. What's more, VIRT can be easily integrated into existing representation-based methods to achieve further improvements.

cs.CL↗

Eco-driving for Electric Connected Vehicles at Signalized Intersections: A Parameterized Reinforcement Learning approach

This paper proposes an eco-driving framework for electric connected vehicles (CVs) based on reinforcement learning (RL) to improve vehicle energy efficiency at signalized intersections. The vehicle agent is specified by integrating the model-based car-following policy, lane-changing policy, and the RL policy, to ensure safe operation of a CV. Subsequently, a Markov Decision Process (MDP) is formulated, which enables the vehicle to perform longitudinal control and lateral decisions, jointly optimizing the car-following and lane-changing behaviors of the CVs in the vicinity of intersections. Then, the hybrid action space is parameterized as a hierarchical structure and thereby trains the agents with two-dimensional motion patterns in a dynamic traffic environment. Finally, our proposed methods are evaluated in SUMO software from both a single-vehicle-based perspective and a flow-based perspective. The results show that our strategy can significantly reduce energy consumption by learning proper action schemes without any interruption of other human-driven vehicles (HDVs).

cs.RO↗

Chaotic diffusion of asteroids in the exterior 1:2 mean motion resonance with Mars

The inner asteroid belt between 2.1 and 2.5 au is of particular dynamical significance because it is the dominant source of both chondritic meteorites and near-Earth asteroids. This inner belt is bounded by an eccentricity-type secular resonance and by the 1:3 mean motion resonance with Jupiter. Unless asteroid perihelia are low enough to allow scattering by Mars, escape requires transport to one of the bounding resonances. In addition Yarkovsky forces are generally ineffective in changing either the eccentricity and/or inclination for asteroids with diameter $\gtrsim$30 km. Thus, large asteroids with pericentres far from Mars may only escape from the inner belt through large changes in their eccentricities. In this paper we study chaotic diffusion of orbits near the 1:2 mean motion resonance with Mars in a systematic way. We show that, while chaotic orbital evolution in both resonant and non-resonant orbits increase the dispersion of the inclinations and eccentricities, it does not significantly change their mean values. We show further that, while the dispersive growth is greatest for resonant orbits, at high $e$ the resonance acts to mitigate asteroid scattering by Mars - making the asteroid lifetime in the belt longer than it would have been for a non-resonant orbit. For asteroids of all sizes in both resonant and non-resonant orbits, the changes in eccentricity needed to account for the observations cannot be achieved by gravitational forces alone. The role of resonant trapping in protecting asteroids from encounters with Mars is also analysed.

astro-ph.EP↗

The primitive equations with magnetic field approximation of the 3D MHD equations

In our earlier work \cite{DLL}, we have shown the global well-posedness of strong solutions to the three-dimensional primitive equations with the magnetic field (PEM) on a thin domain. The heart of this paper is to provide a rigorous justification of the derivation of the PEM as the small aspect ratio limit of the incompressible three-dimensional scaled magnetohydrodynamics (SMHD) equations in the anisotropic horizontal viscosity and magnetic field regime. For the case of $H^1$-initial data case, we prove that global Leray-Hopf weak solutions of the three-dimensional SMHD equation strongly converge to the global strong solutions of the PEM. In the $H^2$-initial data case, the strong solution of the SMHD can be extended to be a global one for small $\v$. As a consequence, we observe that the global strong solutions of the SMHD strong converge to the global strong solutions of the PEM. As a byproduct, the convergence rate is of the same order as the aspect ratio parameter.

math.AP↗

GJ 3929: High Precision Photometric and Doppler Characterization of an Exo-Venus and its Hot, Mini-Neptune-mass Companion

We detail the follow up and characterization of a transiting exo-Venus identified by TESS, GJ 3929b, (TOI-2013b) and its non-transiting companion planet, GJ 3929c (TOI-2013c). GJ 3929b is an Earth-sized exoplanet in its star's Venus-zone (P$_{b}$ = 2.616272 $\pm$ 0.000005 days; S$_{b}$ = 17.3$^{+0.8}_{-0.7}$ S$_{\oplus}$) orbiting a nearby M dwarf. GJ 3929c is most likely a non-transiting sub-Neptune. Using the new, ultra-precise NEID spectrometer on the WIYN 3.5 m Telescope at Kitt Peak National Observatory, we are able to modify the mass constraints of planet b reported in previous works and consequently improve the significance of the mass measurement to almost 4$σ$ confidence (M$_{b}$ = 1.75 $\pm$ 0.45 M$_{\oplus}$). We further adjust the orbital period of planet c from its alias at 14.30 $\pm$ 0.03 days to the likely true period of 15.04 $\pm$ 0.03 days, and adjust its minimum mass to m$\sin i$ = 5.71 $\pm$ 0.92 M$_{\oplus}$. Using the diffuser-assisted ARCTIC imager on the ARC 3.5 m telescope at Apache Point Observatory, in addition to publicly available TESS and LCOGT photometry, we are able to constrain the radius of planet b to R$_{p}$ = 1.09 $\pm$ 0.04 R$_{\oplus}$. GJ 3929b is a top candidate for transmission spectroscopy in its size regime (TSM = 14 $\pm$ 4), and future atmospheric studies of GJ 3929b stand to shed light on the nature of small planets orbiting M dwarfs.

astro-ph.EP↗

A Novel Splitting Criterion Inspired by Geometric Mean Metric Learning for Decision Tree

Decision tree (DT) attracts persistent research attention due to its impressive empirical performance and interpretability in numerous applications. However, the growth of traditional yet widely-used univariate decision trees (UDTs) is quite time-consuming as they need to traverse all the features to find the splitting value with the maximal reduction of the impurity at each internal node. In this paper, we newly design a splitting criterion to speed up the growth. The criterion is induced from Geometric Mean Metric Learning (GMML) and then optimized under its diagonalized metric matrix constraint, consequently, a closed-form rank of feature discriminant abilities can at once be obtained and the top 1 feature at each node used to grow an intent DT (called as dGMML-DT, where d is an abbreviation for diagonalization). We evaluated the performance of the proposed methods and their corresponding ensembles on benchmark datasets. The experiment shows that dGMML-DT achieves comparable or better classification results more efficiently than the UDTs with 10x average speedup. Furthermore, dGMML-DT can straightforwardly be extended to its multivariable counterpart (dGMML-MDT) without needing laborious operations.

cs.LG↗

Global well-posedness of the 3D Primitive Equations with magnetic field

In this paper, the three-dimensional primitive equations with magnetic field (PEM) are considered on a thin domain. We showed the global existence and uniqueness (regularity) of strong solutions to the three-dimensional incompressible PEM without any small assumption on the initial data. More precisely, there exists a unique strong solution globally in time for any given $H^2$-smooth initial data.

math.AP↗