arXiv subjects

Zhicheng Wang

Publications and source records attributed to Zhicheng Wang.

At least 73 records · Page 4Linked to original sources

arXiv2023

Solution multiplicity and effects of data and eddy viscosity on Navier-Stokes solutions inferred by physics-informed neural networks

Physics-informed neural networks (PINNs) have emerged as a new simulation paradigm for fluid flows and are especially effective for inverse and hybrid problems. However, vanilla PINNs often fail in forward problems, especially at high Reynolds (Re) number flows. Herein, we study systematically the classical lid-driven cavity flow at $Re=2,000$, $3,000$ and $5,000$. We observe that vanilla PINNs obtain two classes of solutions, one class that agrees with direct numerical simulations (DNS), and another that is an unstable solution to the Navier-Stokes equations and not physically realizable. We attribute this solution multiplicity to singularities and unbounded vorticity, and we propose regularization methods that restore a unique solution within 1\% difference from the DNS solution. In particular, we introduce a parameterized entropy-viscosity method as artificial eddy viscosity and identify suitable parameters that drive the PINNs solution towards the DNS solution. Furthermore, we solve the inverse problem by subsampling the DNS solution, and identify a new eddy viscosity distribution that leads to velocity and pressure fields almost identical to their DNS counterparts. Surprisingly, a single measurement at a random point suffices to obtain a unique PINNs DNS-like solution even without artificial viscosity, which suggests possible pathways in simulating high Reynolds number turbulent flows using vanilla PINNs.

physics.flu-dyn↗

arXiv2023

Reconstruction-Aware Prior Distillation for Semi-supervised Point Cloud Completion

Real-world sensors often produce incomplete, irregular, and noisy point clouds, making point cloud completion increasingly important. However, most existing completion methods rely on large paired datasets for training, which is labor-intensive. This paper proposes RaPD, a novel semi-supervised point cloud completion method that reduces the need for paired datasets. RaPD utilizes a two-stage training scheme, where a deep semantic prior is learned in stage 1 from unpaired complete and incomplete point clouds, and a semi-supervised prior distillation process is introduced in stage 2 to train a completion network using only a small number of paired samples. Additionally, a self-supervised completion module is introduced to improve performance using unpaired incomplete point clouds. Experiments on multiple datasets show that RaPD outperforms previous methods in both homologous and heterologous scenarios.

cs.CV↗

arXiv2023

Wavefront sets and descent method for finite unitary groups

Let $G$ be a connected reductive algebraic group defined over a finite field $\mathbb{F}_q$. In the 1980s, Kawanaka introduced the generalized Gelfand-Graev representations (GGGRs for short) of the finite group $G^F$ in the case where $q$ is a power of a good prime for $G^F$. An essential feature of GGGRs is that they are very closely related to the (Kawanaka) wavefront sets of the irreducible representations $π$ of $G^F$. In \cite[Theorem 11.2]{L7}, Lusztig showed that if a nilpotent element $X\in G^F$ is ``large'' for an irreducible representation $π$, then the representation $π$ appears with ``small'' multiplicity in the GGGR associated to $X$. In this paper, we prove that for unitary groups, if $X$ is the wavefront of $π$, the multiplicity equals one, which generalizes the multiplicity one result of usual Gelfand-Graev representations. Moreover, we give an algorithm to decompose GGGRs for $\textrm{U}_n(\mathbb{F}_q)$ and calculate the $\textrm{U}_4(\mathbb{F}_q)$ case by this algorithm.

math.RT↗

arXiv2023

POEM: Reconstructing Hand in a Point Embedded Multi-view Stereo

Enable neural networks to capture 3D geometrical-aware features is essential in multi-view based vision tasks. Previous methods usually encode the 3D information of multi-view stereo into the 2D features. In contrast, we present a novel method, named POEM, that directly operates on the 3D POints Embedded in the Multi-view stereo for reconstructing hand mesh in it. Point is a natural form of 3D information and an ideal medium for fusing features across views, as it has different projections on different views. Our method is thus in light of a simple yet effective idea, that a complex 3D hand mesh can be represented by a set of 3D points that 1) are embedded in the multi-view stereo, 2) carry features from the multi-view images, and 3) encircle the hand. To leverage the power of points, we design two operations: point-based feature fusion and cross-set point attention mechanism. Evaluation on three challenging multi-view datasets shows that POEM outperforms the state-of-the-art in hand mesh reconstruction. Code and models are available for research at https://github.com/lixiny/POEM.

cs.CV↗

arXiv2022

Fast Rule-Based Decoding: Revisiting Syntactic Rules in Neural Constituency Parsing

Most recent studies on neural constituency parsing focus on encoder structures, while few developments are devoted to decoders. Previous research has demonstrated that probabilistic statistical methods based on syntactic rules are particularly effective in constituency parsing, whereas syntactic rules are not used during the training of neural models in prior work probably due to their enormous computation requirements. In this paper, we first implement a fast CKY decoding procedure harnessing GPU acceleration, based on which we further derive a syntactic rule-based (rule-constrained) CKY decoding. In the experiments, our method obtains 95.89 and 92.52 F1 on the datasets of PTB and CTB respectively, which shows significant improvements compared with previous approaches. Besides, our parser achieves strong and competitive cross-domain performance in zero-shot settings.

cs.CL↗

arXiv2022

MonoSIM: Simulating Learning Behaviors of Heterogeneous Point Cloud Object Detectors for Monocular 3D Object Detection

Monocular 3D object detection is a fundamental but very important task to many applications including autonomous driving, robotic grasping and augmented reality. Existing leading methods tend to estimate the depth of the input image first, and detect the 3D object based on point cloud. This routine suffers from the inherent gap between depth estimation and object detection. Besides, the prediction error accumulation would also affect the performance. In this paper, a novel method named MonoSIM is proposed. The insight behind introducing MonoSIM is that we propose to simulate the feature learning behaviors of a point cloud based detector for monocular detector during the training period. Hence, during inference period, the learned features and prediction would be similar to the point cloud based detector as possible. To achieve it, we propose one scene-level simulation module, one RoI-level simulation module and one response-level simulation module, which are progressively used for the detector's full feature learning and prediction pipeline. We apply our method to the famous M3D-RPN detector and CaDDN detector, conducting extensive experiments on KITTI and Waymo Open datasets. Results show that our method consistently improves the performance of different monocular detectors for a large margin without changing their network architectures. Our codes will be publicly available at https://github.com/sunh18/MonoSIM}{https://github.com/sunh18/MonoSIM.

cs.CV↗

arXiv2022

Joint Chinese Word Segmentation and Span-based Constituency Parsing

In constituency parsing, span-based decoding is an important direction. However, for Chinese sentences, because of their linguistic characteristics, it is necessary to utilize other models to perform word segmentation first, which introduces a series of uncertainties and generally leads to errors in the computation of the constituency tree afterward. This work proposes a method for joint Chinese word segmentation and Span-based Constituency Parsing by adding extra labels to individual Chinese characters on the parse trees. Through experiments, the proposed algorithm outperforms the recent models for joint segmentation and constituency parsing on CTB 5.1.

cs.CL↗

arXiv2022

Order-sensitive Neural Constituency Parsing

We propose a novel algorithm that improves on the previous neural span-based CKY decoder for constituency parsing. In contrast to the traditional span-based decoding, where spans are combined only based on the sum of their scores, we introduce an order-sensitive strategy, where the span combination scores are more carefully derived from an order-sensitive basis. Our decoder can be regarded as a generalization over existing span-based decoder in determining a finer-grain scoring scheme for the combination of lower-level spans into higher-level spans, where we emphasize on the order of the lower-level spans and use order-sensitive span scores as well as order-sensitive combination grammar rule scores to enhance prediction accuracy. We implement the proposed decoding strategy harnessing GPU parallelism and achieve a decoding speed on par with state-of-the-art span-based parsers. Using the previous state-of-the-art model without additional data as our baseline, we outperform it and improve the F1 score on the Penn Treebank Dataset by 0.26% and on the Chinese Treebank Dataset by 0.35%.

cs.CL↗

arXiv2022

Wavefront sets and descent method for finite symplectic groups

In \cite{JZ1}, D. Jiang and L. Zhang proposed a conjecture which related the wavefront sets and the descent method in the local fields case. Recently, in \cite{JLZ}, they and D. Liu define the arithmetic wavefront set of certain irreducible admissible representation $π$ of a classical group $G(k)$ defined over local field $k$, which is a subset of $k$-rational nilpotent orbits of the Lie algebra of $G(k)$, by the arithmetic structures of the enhanced L-parameter of $π$. These arithmetic structures are based on the rationality of the local Langlands correspondence and the local Gan-Gross-Prasad conjecture. They also prove that the arithmetic wavefront set is an invariant of $π$ (it is independent of the choice of the Whittaker datum \cite[Theorem 1.1]{JLZ}), and propose several conjectures to describe the relationship between arithmetic wavefront sets, analytic wavefront sets and algebraic wavefront sets. In this paper we study wavefront sets of irreducible representations for finite symplectic groups and describe the relationship between wavefront sets, descent method and finite Gan-Gross-Prasad problem. The finite fields case of Gan-Gross-Prasad problem can be calculated explicitly \cite{LW3,Wang1,Wang2}. It allows us to calculate the multiplicity of an irreducible representation in the generalised Gelfand-Graev representation corresponding to certain nilpotent orbits which are finite fields analogies of the arithmetic wavefront sets. In particular, for cuspidal representations, we give certain multiplicity one theorem and show that the finite fields analogy of arithmetic wavefront sets coincides with the wavefront sets in the sense of G. Lusztig and N. Kawanaka.

math.RT↗

arXiv2022

Lusztig correspondence and the Gan-Gross-Prasad problem

The Gan-Gross-Prasad problem is to describe the restriction of representations of a classical group $G$ to smaller groups $H$ of the same kind. In this paper, we solved the Gan-Gross-Prasad problem over finite fields completely. In previous work \cite{LW1,LW2,LW3,Wang}, we study the Gan-Gross-Prasad problem for unipotent representations of finite classical groups. The main tools used are the Lusztig correspondence as well as a formula of Reeder \cite{R} for the pairings of Deligne-Lusztig characters. We give a reduction decomposition of Reeder's formula, and deduce the Gan-Gross-Prasad problem for arbitrary representations from the unipotent representations by Lusztig correspondence.

math.RT↗

arXiv2022

Object Level Depth Reconstruction for Category Level 6D Object Pose Estimation From Monocular RGB Image

Recently, RGBD-based category-level 6D object pose estimation has achieved promising improvement in performance, however, the requirement of depth information prohibits broader applications. In order to relieve this problem, this paper proposes a novel approach named Object Level Depth reconstruction Network (OLD-Net) taking only RGB images as input for category-level 6D object pose estimation. We propose to directly predict object-level depth from a monocular RGB image by deforming the category-level shape prior into object-level depth and the canonical NOCS representation. Two novel modules named Normalized Global Position Hints (NGPH) and Shape-aware Decoupled Depth Reconstruction (SDDR) module are introduced to learn high fidelity object-level depth and delicate shape representations. At last, the 6D object pose is solved by aligning the predicted canonical representation with the back-projected object-level depth. Extensive experiments on the challenging CAMERA25 and REAL275 datasets indicate that our model, though simple, achieves state-of-the-art performance.

cs.CV↗

arXiv2022

SimCC: a Simple Coordinate Classification Perspective for Human Pose Estimation

The 2D heatmap-based approaches have dominated Human Pose Estimation (HPE) for years due to high performance. However, the long-standing quantization error problem in the 2D heatmap-based methods leads to several well-known drawbacks: 1) The performance for the low-resolution inputs is limited; 2) To improve the feature map resolution for higher localization precision, multiple costly upsampling layers are required; 3) Extra post-processing is adopted to reduce the quantization error. To address these issues, we aim to explore a brand new scheme, called \textit{SimCC}, which reformulates HPE as two classification tasks for horizontal and vertical coordinates. The proposed SimCC uniformly divides each pixel into several bins, thus achieving \emph{sub-pixel} localization precision and low quantization error. Benefiting from that, SimCC can omit additional refinement post-processing and exclude upsampling layers under certain settings, resulting in a more simple and effective pipeline for HPE. Extensive experiments conducted over COCO, CrowdPose, and MPII datasets show that SimCC outperforms heatmap-based counterparts, especially in low-resolution settings by a large margin.

cs.CV↗

arXiv2021

Attend to Who You Are: Supervising Self-Attention for Keypoint Detection and Instance-Aware Association

This paper presents a new method to solve keypoint detection and instance association by using Transformer. For bottom-up multi-person pose estimation models, they need to detect keypoints and learn associative information between keypoints. We argue that these problems can be entirely solved by Transformer. Specifically, the self-attention in Transformer measures dependencies between any pair of locations, which can provide association information for keypoints grouping. However, the naive attention patterns are still not subjectively controlled, so there is no guarantee that the keypoints will always attend to the instances to which they belong. To address it we propose a novel approach of supervising self-attention for multi-person keypoint detection and instance association. By using instance masks to supervise self-attention to be instance-aware, we can assign the detected keypoints to their corresponding instances based on the pairwise attention scores, without using pre-defined offset vector fields or embedding like CNN-based bottom-up models. An additional benefit of our method is that the instance segmentation results of any number of people can be directly obtained from the supervised attention matrix, thereby simplifying the pixel assignment pipeline. The experiments on the COCO multi-person keypoint detection challenge and person instance segmentation task demonstrate the effectiveness and simplicity of the proposed method and show a promising way to control self-attention behavior for specific purposes.

cs.CV↗

arXiv2021

ACR-Pose: Adversarial Canonical Representation Reconstruction Network for Category Level 6D Object Pose Estimation

Recently, category-level 6D object pose estimation has achieved significant improvements with the development of reconstructing canonical 3D representations. However, the reconstruction quality of existing methods is still far from excellent. In this paper, we propose a novel Adversarial Canonical Representation Reconstruction Network named ACR-Pose. ACR-Pose consists of a Reconstructor and a Discriminator. The Reconstructor is primarily composed of two novel sub-modules: Pose-Irrelevant Module (PIM) and Relational Reconstruction Module (RRM). PIM tends to learn canonical-related features to make the Reconstructor insensitive to rotation and translation, while RRM explores essential relational information between different input modalities to generate high-quality features. Subsequently, a Discriminator is employed to guide the Reconstructor to generate realistic canonical representations. The Reconstructor and the Discriminator learn to optimize through adversarial training. Experimental results on the prevalent NOCS-CAMERA and NOCS-REAL datasets demonstrate that our method achieves state-of-the-art performance.

cs.CV↗

arXiv2021

On the Gan-Gross-Prasad problem for finite classical groups

In this paper we study the Gan-Gross-Prasad problem for finite classical groups. Our results provide complete answers for unipotent representations, and we obtain the explicit branching laws for these representations. Moreover, for arbitrary representations, we give a formula to reduce the Gan-Gross-Prasad problem to the restriction problem of Deligne-Lusztig characters.

math.RT↗

arXiv2021

Guiding Query Position and Performing Similar Attention for Transformer-Based Detection Heads

After DETR was proposed, this novel transformer-based detection paradigm which performs several cross-attentions between object queries and feature maps for predictions has subsequently derived a series of transformer-based detection heads. These models iterate object queries after each cross-attention. However, they don't renew the query position which indicates object queries' position information. Thus model needs extra learning to figure out the newest regions that query position should express and need more attention. To fix this issue, we propose the Guided Query Position (GQPos) method to embed the latest location information of object queries to query position iteratively. Another problem of such transformer-based detection heads is the high complexity to perform attention on multi-scale feature maps, which hinders them from improving detection performance at all scales. Therefore we propose a novel fusion scheme named Similar Attention (SiA): besides the feature maps is fused, SiA also fuse the attention weights maps to accelerate the learning of high-resolution attention weight map by well-learned low-resolution attention weight map. Our experiments show that the proposed GQPos improves the performance of a series of models, including DETR, SMCA, YoloS, and HoiTransformer and SiA consistently improve the performance of multi-scale transformer-based detection heads like DETR and HoiTransformer.

cs.CV↗

arXiv2021

TokenPose: Learning Keypoint Tokens for Human Pose Estimation

Human pose estimation deeply relies on visual clues and anatomical constraints between parts to locate keypoints. Most existing CNN-based methods do well in visual representation, however, lacking in the ability to explicitly learn the constraint relationships between keypoints. In this paper, we propose a novel approach based on Token representation for human Pose estimation~(TokenPose). In detail, each keypoint is explicitly embedded as a token to simultaneously learn constraint relationships and appearance cues from images. Extensive experiments show that the small and large TokenPose models are on par with state-of-the-art CNN-based counterparts while being more lightweight. Specifically, our TokenPose-S and TokenPose-L achieve $72.5$ AP and $75.8$ AP on COCO validation dataset respectively, with significant reduction in parameters ($\downarrow80.6\%$; $\downarrow$ $56.8\%$) and GFLOPs ($\downarrow$ $75.3\%$; $\downarrow$ $24.7\%$). Code is publicly available.

cs.CV↗

arXiv2021

Adaptive Dilated Convolution For Human Pose Estimation

Most existing human pose estimation (HPE) methods exploit multi-scale information by fusing feature maps of four different spatial sizes, \ie $1/4$, $1/8$, $1/16$, and $1/32$ of the input image. There are two drawbacks of this strategy: 1) feature maps of different spatial sizes may be not well aligned spatially, which potentially hurts the accuracy of keypoint location; 2) these scales are fixed and inflexible, which may restrict the generalization ability over various human sizes. Towards these issues, we propose an adaptive dilated convolution (ADC). It can generate and fuse multi-scale features of the same spatial sizes by setting different dilation rates for different channels. More importantly, these dilation rates are generated by a regression module. It enables ADC to adaptively adjust the fused scales and thus ADC may generalize better to various human sizes. ADC can be end-to-end trained and easily plugged into existing methods. Extensive experiments show that ADC can bring consistent improvements to various HPE methods. The source codes will be released for further research.

cs.CV↗