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Shiquan Zhang

Publications and source records attributed to Shiquan Zhang.

31 records · Page 2Linked to original sources
arXiv2023

Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems

In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential operator is realized by automatic differentiation. The eigenfunction of the eigenvalue problem is learned by the neural network and the iterative algorithms are implemented by optimizing the specially defined loss function. The largest positive eigenvalue, smallest eigenvalue and interior eigenvalues with the given prior knowledge can be solved efficiently. We examine the applicability and accuracy of our methods in the numerical experiments in one dimension, two dimensions and higher dimensions. Numerical results show that accurate eigenvalue and eigenfunction approximations can be obtained by our methods.

math.NA↗
arXiv2023

V-Guard: An Efficient Permissioned Blockchain for Achieving Consensus under Dynamic Memberships in V2X

This paper presents V-Guard, a new permissioned blockchain that achieves consensus for vehicular data under changing memberships, targeting the problem in V2X networks where vehicles are often intermittently connected on the roads. To achieve this goal, V-Guard integrates membership management into the consensus process for agreeing on data entries. It binds a data entry with a membership configuration profile that describes responsible vehicles for achieving consensus for the data entry. As such, V-Guard produces chained consensus results of both data entries and their residing membership profiles, which enables consensus to be achieved seamlessly under changing memberships. In addition, V-Guard separates the ordering of transactions from consensus, allowing concurrent ordering instances and periodic consensus instances to order and commit data entries. These features make V-Guard efficient for achieving consensus under dynamic memberships with high throughput and latency performance.

cs.DC↗
arXiv2023

On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem

In practical engineering experiments, the data obtained through detectors are inevitably noisy. For the already proposed data-enabled physics-informed neural network (DEPINN) \citep{DEPINN}, we investigate the performance of DEPINN in calculating the neutron diffusion eigenvalue problem from several perspectives when the prior data contain different scales of noise. Further, in order to reduce the effect of noise and improve the utilization of the noisy prior data, we propose innovative interval loss functions and give some rigorous mathematical proofs. The robustness of DEPINN is examined on two typical benchmark problems through a large number of numerical results, and the effectiveness of the proposed interval loss function is demonstrated by comparison. This paper confirms the feasibility of the improved DEPINN for practical engineering applications in nuclear reactor physics.

cs.LG↗
arXiv2022

BEVDistill: Cross-Modal BEV Distillation for Multi-View 3D Object Detection

3D object detection from multiple image views is a fundamental and challenging task for visual scene understanding. Owing to its low cost and high efficiency, multi-view 3D object detection has demonstrated promising application prospects. However, accurately detecting objects through perspective views is extremely difficult due to the lack of depth information. Current approaches tend to adopt heavy backbones for image encoders, making them inapplicable for real-world deployment. Different from the images, LiDAR points are superior in providing spatial cues, resulting in highly precise localization. In this paper, we explore the incorporation of LiDAR-based detectors for multi-view 3D object detection. Instead of directly training a depth prediction network, we unify the image and LiDAR features in the Bird-Eye-View (BEV) space and adaptively transfer knowledge across non-homogenous representations in a teacher-student paradigm. To this end, we propose \textbf{BEVDistill}, a cross-modal BEV knowledge distillation (KD) framework for multi-view 3D object detection. Extensive experiments demonstrate that the proposed method outperforms current KD approaches on a highly-competitive baseline, BEVFormer, without introducing any extra cost in the inference phase. Notably, our best model achieves 59.4 NDS on the nuScenes test leaderboard, achieving new state-of-the-art in comparison with various image-based detectors. Code will be available at https://github.com/zehuichen123/BEVDistill.

cs.CV↗
arXiv2022

A data-enabled physics-informed neural network with comprehensive numerical study on solving neutron diffusion eigenvalue problems

We present a data-enabled physics-informed neural network (DEPINN) with comprehensive numerical study for solving industrial scale neutron diffusion eigenvalue problems (NDEPs). In order to achieve an engineering acceptable accuracy for complex engineering problems, a very small amount of prior data from physical experiments are suggested to be used, to improve the accuracy and efficiency of training. We design an adaptive optimization procedure with Adam and LBFGS to accelerate the convergence in the training stage. We discuss the effect of different physical parameters, sampling techniques, loss function allocation and the generalization performance of the proposed DEPINN model for solving complex problem. The feasibility of proposed DEPINN model is tested on three typical benchmark problems, from simple geometry to complex geometry, and from mono-energetic equation to two-group equations. Numerous numerical results show that DEPINN can efficiently solve NDEPs with an appropriate optimization procedure. The proposed DEPINN can be generalized for other input parameter settings once its structure been trained. This work confirms the possibility of DEPINN for practical engineering applications in nuclear reactor physics.

physics.comp-ph↗
arXiv2022

AutoAlignV2: Deformable Feature Aggregation for Dynamic Multi-Modal 3D Object Detection

Point clouds and RGB images are two general perceptional sources in autonomous driving. The former can provide accurate localization of objects, and the latter is denser and richer in semantic information. Recently, AutoAlign presents a learnable paradigm in combining these two modalities for 3D object detection. However, it suffers from high computational cost introduced by the global-wise attention. To solve the problem, we propose Cross-Domain DeformCAFA module in this work. It attends to sparse learnable sampling points for cross-modal relational modeling, which enhances the tolerance to calibration error and greatly speeds up the feature aggregation across different modalities. To overcome the complex GT-AUG under multi-modal settings, we design a simple yet effective cross-modal augmentation strategy on convex combination of image patches given their depth information. Moreover, by carrying out a novel image-level dropout training scheme, our model is able to infer in a dynamic manner. To this end, we propose AutoAlignV2, a faster and stronger multi-modal 3D detection framework, built on top of AutoAlign. Extensive experiments on nuScenes benchmark demonstrate the effectiveness and efficiency of AutoAlignV2. Notably, our best model reaches 72.4 NDS on nuScenes test leaderboard, achieving new state-of-the-art results among all published multi-modal 3D object detectors. Code will be available at https://github.com/zehuichen123/AutoAlignV2.

cs.CV↗
arXiv2022

Graph-DETR3D: Rethinking Overlapping Regions for Multi-View 3D Object Detection

3D object detection from multiple image views is a fundamental and challenging task for visual scene understanding. Due to its low cost and high efficiency, multi-view 3D object detection has demonstrated promising application prospects. However, accurately detecting objects through perspective views in the 3D space is extremely difficult due to the lack of depth information. Recently, DETR3D introduces a novel 3D-2D query paradigm in aggregating multi-view images for 3D object detection and achieves state-of-the-art performance. In this paper, with intensive pilot experiments, we quantify the objects located at different regions and find that the "truncated instances" (i.e., at the border regions of each image) are the main bottleneck hindering the performance of DETR3D. Although it merges multiple features from two adjacent views in the overlapping regions, DETR3D still suffers from insufficient feature aggregation, thus missing the chance to fully boost the detection performance. In an effort to tackle the problem, we propose Graph-DETR3D to automatically aggregate multi-view imagery information through graph structure learning (GSL). It constructs a dynamic 3D graph between each object query and 2D feature maps to enhance the object representations, especially at the border regions. Besides, Graph-DETR3D benefits from a novel depth-invariant multi-scale training strategy, which maintains the visual depth consistency by simultaneously scaling the image size and the object depth. Extensive experiments on the nuScenes dataset demonstrate the effectiveness and efficiency of our Graph-DETR3D. Notably, our best model achieves 49.5 NDS on the nuScenes test leaderboard, achieving new state-of-the-art in comparison with various published image-view 3D object detectors.

cs.CV↗
arXiv2022

AutoAlign: Pixel-Instance Feature Aggregation for Multi-Modal 3D Object Detection

Object detection through either RGB images or the LiDAR point clouds has been extensively explored in autonomous driving. However, it remains challenging to make these two data sources complementary and beneficial to each other. In this paper, we propose \textit{AutoAlign}, an automatic feature fusion strategy for 3D object detection. Instead of establishing deterministic correspondence with camera projection matrix, we model the mapping relationship between the image and point clouds with a learnable alignment map. This map enables our model to automate the alignment of non-homogenous features in a dynamic and data-driven manner. Specifically, a cross-attention feature alignment module is devised to adaptively aggregate \textit{pixel-level} image features for each voxel. To enhance the semantic consistency during feature alignment, we also design a self-supervised cross-modal feature interaction module, through which the model can learn feature aggregation with \textit{instance-level} feature guidance. Extensive experimental results show that our approach can lead to 2.3 mAP and 7.0 mAP improvements on the KITTI and nuScenes datasets, respectively. Notably, our best model reaches 70.9 NDS on the nuScenes testing leaderboard, achieving competitive performance among various state-of-the-arts.

cs.CV↗
arXiv2017

An Optimal Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems

The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from discontinuous functions to continuous ones, and adopts piecewise polynomials of equal degrees on simplex meshes for all variables. In this paper, we analyze a new EDG method for second order elliptic problems on polygonal/polyhedral meshes. By using piecewise polynomials of degrees $k+1$, $k+1$, $k$ ($k\geq 0$) to approximate the potential, numerical trace and flux, respectively, the new method is shown to yield optimal convergence rates for both the potential and flux approximations. Numerical experiments are provided to confirm the theoretical results.

math.NA↗
arXiv2015

Analysis of a two-level algorithm for HDG methods for diffusion problems

This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate of the algorithm, and show that the theoretical results also apply to weak Galerkin (WG) methods. The main features of our analysis are twofold: one is that we only need the minimal regularity of the model problem; the other is that we do not require the triangulations to be quasi-uniform. Numerical experiments are provided to confirm the theoretical results.

math.NA↗
arXiv2014

A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries

In order to achieve a better understanding of degradation processes in lithium-ion batteries, the modelling of cell dynamics at the mircometer scale is an important focus of current mathematical research. These models lead to large-dimensional, highly nonlinear finite volume discretizations which, due to their complexity, cannot be solved at cell scale on current hardware. Model order reduction strategies are therefore necessary to reduce the computational complexity while retaining the features of the model. The application of such strategies to specialized high performance solvers asks for new software designs allowing flexible control of the solvers by the reduction algorithms. In this contribution we discuss the reduction of microscale battery models with the reduced basis method and report on our new software approach on integrating the model order reduction software pyMOR with third-party solvers. Finally, we present numerical results for the reduction of a 3D microscale battery model with porous electrode geometry.

math.NA↗
arXiv2013

Combined Preconditioning with Applications in Reservoir Simulation

We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner. The resulting preconditioner, which we refer to as a combined preconditioner, is much more robust and efficient than the iterative method and preconditioner when used in Krylov subspace methods. We prove that the combined preconditioner is positive definite and show estimates on the condition number of the preconditioned system. We combine an algebraic multigrid method and an incomplete factorization preconditioner to test the proposed framework on problems in petroleum reservoir simulation. Our numerical experiments demonstrate noticeable speed-up when we compare our combined method with the standalone algebraic multigrid method or the incomplete factorization preconditioner.

math.NA↗