arXiv subjects

Qian Zhang

Publications and source records attributed to Qian Zhang.

At least 253 records · Page 14Linked to original sources

arXiv2023

Distributional Hessian and divdiv complexes on triangulation and cohomology

In this paper, we construct discrete versions of some Bernstein-Gelfand-Gelfand (BGG) complexes, i.e., the Hessian and the divdiv complexes, on triangulations in 2D and 3D. The sequences consist of finite elements with local polynomial shape functions and various types of Dirac measure on subsimplices. The construction generalizes Whitney forms (canonical conforming finite elements) for the de Rham complex and Regge calculus/finite elements for the elasticity (Riemannian deformation) complex from discrete topological and Discrete Exterior Calculus perspectives. We show that the cohomology of the resulting complexes is isomorphic to the continuous versions, and thus isomorphic to the de~Rham cohomology with coefficients.

math.NA↗

arXiv2023

Unfitted finite element method for the quad-curl interface problem

In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure stability, we incorporate ghost penalty terms and a discrete divergence-free term. We establish the well-posedness of our method and demonstrate an optimal error bound in the discrete energy norm. We also analyze the stiffness matrix's condition number. Our numerical tests back up our theory on convergence rates and condition numbers.

math.NA↗

arXiv2023

A Systematical Evaluation for Next-Basket Recommendation Algorithms

Next basket recommender systems (NBRs) aim to recommend a user's next (shopping) basket of items via modeling the user's preferences towards items based on the user's purchase history, usually a sequence of historical baskets. Due to its wide applicability in the real-world E-commerce industry, the studies NBR have attracted increasing attention in recent years. NBRs have been widely studied and much progress has been achieved in this area with a variety of NBR approaches having been proposed. However, an important issue is that there is a lack of a systematic and unified evaluation over the various NBR approaches. Different studies often evaluate NBR approaches on different datasets, under different experimental settings, making it hard to fairly and effectively compare the performance of different NBR approaches. To bridge this gap, in this work, we conduct a systematical empirical study in NBR area. Specifically, we review the representative work in NBR and analyze their cons and pros. Then, we run the selected NBR algorithms on the same datasets, under the same experimental setting and evaluate their performances using the same measurements. This provides a unified framework to fairly compare different NBR approaches. We hope this study can provide a valuable reference for the future research in this vibrant area.

cs.IR↗

arXiv2023

A locking-free mixed enriched Galerkin method of arbitrary order for linear elasticity using the stress-displacement formulation

In this paper, we develop an arbitrary-order locking-free enriched Galerkin method for the linear elasticity problem using the stress-displacement formulation in both two and three dimensions. The method is based on the mixed discontinuous Galerkin method in [30], but with a different stress approximation space that enriches the arbitrary order continuous Galerkin space with some piecewise symmetric-matrix valued polynomials. We prove that the method is well-posed and provide a parameter-robust error estimate, which confirms the locking-free property of the EG method. We present some numerical examples in two and three dimensions to demonstrate the effectiveness of the proposed method.

math.NA↗

arXiv2023

A Gronwall Inequality Based Approach to Transient Stability Assessment for Power Grids

This paper proposes a novel Gronwall inequality-based method for transient stability assessment for power systems. The challenges of applying such methods to power systems are how to construct the differential inequality and how to treat its nonlinearity. By leveraging partial derivatives, a rotor angle difference inequality model is established, and the difficulty of nonlinearity of this model is solved by piecewise linearization. Based on our method, the upper bound of the rotor angle difference is given analytically, which can be used to estimate the stability boundary, i.e. the critical clearing time (CCT) of power systems. A case study on the IEEE 9-bus system shows the accuracy of the approach in early warning of transient instability for power grids.

eess.SY↗

arXiv2023

Circuit as Set of Points

As the size of circuit designs continues to grow rapidly, artificial intelligence technologies are being extensively used in Electronic Design Automation (EDA) to assist with circuit design. Placement and routing are the most time-consuming parts of the physical design process, and how to quickly evaluate the placement has become a hot research topic. Prior works either transformed circuit designs into images using hand-crafted methods and then used Convolutional Neural Networks (CNN) to extract features, which are limited by the quality of the hand-crafted methods and could not achieve end-to-end training, or treated the circuit design as a graph structure and used Graph Neural Networks (GNN) to extract features, which require time-consuming preprocessing. In our work, we propose a novel perspective for circuit design by treating circuit components as point clouds and using Transformer-based point cloud perception methods to extract features from the circuit. This approach enables direct feature extraction from raw data without any preprocessing, allows for end-to-end training, and results in high performance. Experimental results show that our method achieves state-of-the-art performance in congestion prediction tasks on both the CircuitNet and ISPD2015 datasets, as well as in design rule check (DRC) violation prediction tasks on the CircuitNet dataset. Our method establishes a bridge between the relatively mature point cloud perception methods and the fast-developing EDA algorithms, enabling us to leverage more collective intelligence to solve this task. To facilitate the research of open EDA design, source codes and pre-trained models are released at https://github.com/hustvl/circuitformer.

cs.CV↗

arXiv2023

Redistributing the Precision and Content in 3D-LUT-based Inverse Tone-mapping for HDR/WCG Display

ITM(inverse tone-mapping) converts SDR (standard dynamic range) footage to HDR/WCG (high dynamic range /wide color gamut) for media production. It happens not only when remastering legacy SDR footage in front-end content provider, but also adapting on-theair SDR service on user-end HDR display. The latter requires more efficiency, thus the pre-calculated LUT (look-up table) has become a popular solution. Yet, conventional fixed LUT lacks adaptability, so we learn from research community and combine it with AI. Meanwhile, higher-bit-depth HDR/WCG requires larger LUT than SDR, so we consult traditional ITM for an efficiency-performance trade-off: We use 3 smaller LUTs, each has a non-uniform packing (precision) respectively denser in dark, middle and bright luma range. In this case, their results will have less error only in their own range, so we use a contribution map to combine their best parts to final result. With the guidance of this map, the elements (content) of 3 LUTs will also be redistributed during training. We conduct ablation studies to verify method's effectiveness, and subjective and objective experiments to show its practicability. Code is available at: https://github.com/AndreGuo/ITMLUT.

cs.MM↗

arXiv2023

On Convergence of Federated Averaging Langevin Dynamics

We propose a federated averaging Langevin algorithm (FA-LD) for uncertainty quantification and mean predictions with distributed clients. In particular, we generalize beyond normal posterior distributions and consider a general class of models. We develop theoretical guarantees for FA-LD for strongly log-concave distributions with non-i.i.d data and study how the injected noise and the stochastic-gradient noise, the heterogeneity of data, and the varying learning rates affect the convergence. Such an analysis sheds light on the optimal choice of local updates to minimize communication costs. Important to our approach is that the communication efficiency does not deteriorate with the injected noise in the Langevin algorithms. In addition, we examine in our FA-LD algorithm both independent and correlated noise used over different clients. We observe there is a trade-off between the pairs among communication, accuracy, and data privacy. As local devices may become inactive in federated networks, we also show convergence results based on different averaging schemes where only partial device updates are available. In such a case, we discover an additional bias that does not decay to zero.

stat.ML↗

arXiv2023

FireFly v2: Advancing Hardware Support for High-Performance Spiking Neural Network with a Spatiotemporal FPGA Accelerator

Spiking Neural Networks (SNNs) are expected to be a promising alternative to Artificial Neural Networks (ANNs) due to their strong biological interpretability and high energy efficiency. Specialized SNN hardware offers clear advantages over general-purpose devices in terms of power and performance. However, there's still room to advance hardware support for state-of-the-art (SOTA) SNN algorithms and improve computation and memory efficiency. As a further step in supporting high-performance SNNs on specialized hardware, we introduce FireFly v2, an FPGA SNN accelerator that can address the issue of non-spike operation in current SOTA SNN algorithms, which presents an obstacle in the end-to-end deployment onto existing SNN hardware. To more effectively align with the SNN characteristics, we design a spatiotemporal dataflow that allows four dimensions of parallelism and eliminates the need for membrane potential storage, enabling on-the-fly spike processing and spike generation. To further improve hardware acceleration performance, we develop a high-performance spike computing engine as a backend based on a systolic array operating at 500-600MHz. To the best of our knowledge, FireFly v2 achieves the highest clock frequency among all FPGA-based implementations. Furthermore, it stands as the first SNN accelerator capable of supporting non-spike operations, which are commonly used in advanced SNN algorithms. FireFly v2 has doubled the throughput and DSP efficiency when compared to our previous version of FireFly and it exhibits 1.33 times the DSP efficiency and 1.42 times the power efficiency compared to the current most advanced FPGA accelerators.

cs.NE↗

arXiv2023

Techno-Economic Analysis of Synthetic Fuel Production from Existing Nuclear Power Plants across the United States

Low carbon synfuel can displace transport fossil fuels such as diesel and jet fuel and help achieve the decarbonization of the transportation sector at a global scale, but large-scale cost-effective production facilities are needed. Meanwhile, nuclear power plants are closing due to economic difficulties: electricity prices are too low and variable to cover their operational costs. Using existing nuclear power plants to produce synfuels might prevent loss of these low-carbon assets while producing synfuels at scale, but no technoeconomic analysis of this Integrated Energy System exist. We quantify the technoeconomic potential of coupling a synthetic fuel production process with five example nuclear power plants across the U.S. to explore the influence of different electricity markets, access to carbon dioxide sources, and fuel markets. Coupling synfuel production increases nuclear plant profitability by up to 792 million USD(2020) in addition to a 10 percent rate of return on investment over a 20 year period. Our analysis identifies drivers for the economic profitability of the synfuel IES. The hydrogen production tax credit from the 2022 Inflation Reduction Act is essential to its overall profitability representing on average three quarters of its revenues. The carbon feedstock transportation is the highest cost - more than a third on average - closely followed by the synfuel production process capital costs. Those results show the key role of incentive policies for the decarbonization of the transportation sector and the economic importance of the geographic location of Integrated Energy Systems.

econ.GN↗

arXiv2023

AI Mobile Application for Archaeological Dating of Bronze Dings

We develop an AI application for archaeological dating of bronze Dings. A classification model is employed to predict the period of the input Ding, and a detection model is used to show the feature parts for making a decision of archaeological dating. To train the two deep learning models, we collected a large number of Ding images from published materials, and annotated the period and the feature parts on each image by archaeological experts. Furthermore, we design a user system and deploy our pre-trained models based on the platform of WeChat Mini Program for ease of use. Only need a smartphone installed WeChat APP, users can easily know the result of intelligent archaeological dating, the feature parts, and other reference artifacts, by taking a photo of a bronze Ding. To use our application, please scan this QR code by WeChat.

cs.CV↗

arXiv2023

Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning

We introduce a method to convert Physics-Informed Neural Networks (PINNs), commonly used in scientific machine learning, to Spiking Neural Networks (SNNs), which are expected to have higher energy efficiency compared to traditional Artificial Neural Networks (ANNs). We first extend the calibration technique of SNNs to arbitrary activation functions beyond ReLU, making it more versatile, and we prove a theorem that ensures the effectiveness of the calibration. We successfully convert PINNs to SNNs, enabling computational efficiency for diverse regression tasks in solving multiple differential equations, including the unsteady Navier-Stokes equations. We demonstrate great gains in terms of overall efficiency, including Separable PINNs (SPINNs), which accelerate the training process. Overall, this is the first work of this kind and the proposed method achieves relatively good accuracy with low spike rates.

cs.NE↗

arXiv2023

Improving Few-shot Image Generation by Structural Discrimination and Textural Modulation

Few-shot image generation, which aims to produce plausible and diverse images for one category given a few images from this category, has drawn extensive attention. Existing approaches either globally interpolate different images or fuse local representations with pre-defined coefficients. However, such an intuitive combination of images/features only exploits the most relevant information for generation, leading to poor diversity and coarse-grained semantic fusion. To remedy this, this paper proposes a novel textural modulation (TexMod) mechanism to inject external semantic signals into internal local representations. Parameterized by the feedback from the discriminator, our TexMod enables more fined-grained semantic injection while maintaining the synthesis fidelity. Moreover, a global structural discriminator (StructD) is developed to explicitly guide the model to generate images with reasonable layout and outline. Furthermore, the frequency awareness of the model is reinforced by encouraging the model to distinguish frequency signals. Together with these techniques, we build a novel and effective model for few-shot image generation. The effectiveness of our model is identified by extensive experiments on three popular datasets and various settings. Besides achieving state-of-the-art synthesis performance on these datasets, our proposed techniques could be seamlessly integrated into existing models for a further performance boost.

cs.CV↗

arXiv2023

VMA: Divide-and-Conquer Vectorized Map Annotation System for Large-Scale Driving Scene

High-definition (HD) map serves as the essential infrastructure of autonomous driving. In this work, we build up a systematic vectorized map annotation framework (termed VMA) for efficiently generating HD map of large-scale driving scene. We design a divide-and-conquer annotation scheme to solve the spatial extensibility problem of HD map generation, and abstract map elements with a variety of geometric patterns as unified point sequence representation, which can be extended to most map elements in the driving scene. VMA is highly efficient and extensible, requiring negligible human effort, and flexible in terms of spatial scale and element type. We quantitatively and qualitatively validate the annotation performance on real-world urban and highway scenes, as well as NYC Planimetric Database. VMA can significantly improve map generation efficiency and require little human effort. On average VMA takes 160min for annotating a scene with a range of hundreds of meters, and reduces 52.3% of the human cost, showing great application value. Code: https://github.com/hustvl/VMA.

cs.CV↗

arXiv2023

VAD: Vectorized Scene Representation for Efficient Autonomous Driving

Autonomous driving requires a comprehensive understanding of the surrounding environment for reliable trajectory planning. Previous works rely on dense rasterized scene representation (e.g., agent occupancy and semantic map) to perform planning, which is computationally intensive and misses the instance-level structure information. In this paper, we propose VAD, an end-to-end vectorized paradigm for autonomous driving, which models the driving scene as a fully vectorized representation. The proposed vectorized paradigm has two significant advantages. On one hand, VAD exploits the vectorized agent motion and map elements as explicit instance-level planning constraints which effectively improves planning safety. On the other hand, VAD runs much faster than previous end-to-end planning methods by getting rid of computation-intensive rasterized representation and hand-designed post-processing steps. VAD achieves state-of-the-art end-to-end planning performance on the nuScenes dataset, outperforming the previous best method by a large margin. Our base model, VAD-Base, greatly reduces the average collision rate by 29.0% and runs 2.5x faster. Besides, a lightweight variant, VAD-Tiny, greatly improves the inference speed (up to 9.3x) while achieving comparable planning performance. We believe the excellent performance and the high efficiency of VAD are critical for the real-world deployment of an autonomous driving system. Code and models are available at https://github.com/hustvl/VAD for facilitating future research.

cs.RO↗

arXiv2023

Conditional Perceptual Quality Preserving Image Compression

We propose conditional perceptual quality, an extension of the perceptual quality defined in \citet{blau2018perception}, by conditioning it on user defined information. Specifically, we extend the original perceptual quality $d(p_{X},p_{\hat{X}})$ to the conditional perceptual quality $d(p_{X|Y},p_{\hat{X}|Y})$, where $X$ is the original image, $\hat{X}$ is the reconstructed, $Y$ is side information defined by user and $d(.,.)$ is divergence. We show that conditional perceptual quality has similar theoretical properties as rate-distortion-perception trade-off \citep{blau2019rethinking}. Based on these theoretical results, we propose an optimal framework for conditional perceptual quality preserving compression. Experimental results show that our codec successfully maintains high perceptual quality and semantic quality at all bitrate. Besides, by providing a lowerbound of common randomness required, we settle the previous arguments on whether randomness should be incorporated into generator for (conditional) perceptual quality compression. The source code is provided in supplementary material.

eess.IV↗

arXiv2023

Interpretable Motion Planner for Urban Driving via Hierarchical Imitation Learning

Learning-based approaches have achieved remarkable performance in the domain of autonomous driving. Leveraging the impressive ability of neural networks and large amounts of human driving data, complex patterns and rules of driving behavior can be encoded as a model to benefit the autonomous driving system. Besides, an increasing number of data-driven works have been studied in the decision-making and motion planning module. However, the reliability and the stability of the neural network is still full of uncertainty. In this paper, we introduce a hierarchical planning architecture including a high-level grid-based behavior planner and a low-level trajectory planner, which is highly interpretable and controllable. As the high-level planner is responsible for finding a consistent route, the low-level planner generates a feasible trajectory. We evaluate our method both in closed-loop simulation and real world driving, and demonstrate the neural network planner has outstanding performance in complex urban autonomous driving scenarios.

cs.RO↗

arXiv2023

On the stability of critical points of the Hardy-Littlewood-Sobolev inequality

This paper is concerned with the quantitative stability of critical points of the Hardy-Littlewood-Sobolev inequality. Namely, we give quantitative estimates for the Choquard equation: $$-Δu=(I_μ\ast|u|^{2_μ^*}) u^{2_μ^*-1}\ \ \text{in}\ \ \R^N,$$ where $u>0,\ N\geq 3,\ μ\in(0,N)$, $I_μ$ is the Riesz potential and $2_μ^* \coloneqq \frac{2N-μ}{N-2}$ is the upper Hardy-Littlewood-Sobolev critical exponent. The Struwe's decomposition (see M. Struwe: Math Z.,1984) showed that the equation $Δu + u^{\frac{N+2}{N-2 }}=0$ has phenomenon of ``stable up to bubbling'', that is, if $u\geq0$ and $\|Δu+u^{\frac{N+2}{N-2}}\|_{(\mathcal{D}^{1,2})^{-1}}$ approaches zero, then $d(u)$ goes to zero, where $d(u)$ denotes the $\mathcal{D}^{1,2}(\R^N)$-distance between $u$ and the set of all sums of Talenti bubbles. Ciraolo, F{}igalli and Maggi (Int. Math. Res. Not.,2017) obtained the f{}irst quantitative version of Struwe's decomposition with single bubble in all dimensions $N\geq 3$, i.e, $\displaystyle d(u)\leq C\|Δu+u^{\frac{N+2}{N-2}}\|_{L^{\frac{2N}{N+2}}}.$ For multiple bubbles, F{}igalli and Glaudo (Arch. Rational Mech. Anal., 2020) obtained quantitative estimates depending on the dimension, namely $$ d(u)\leq C\|Δu+u^{\frac{N+2}{N-2}}\|_{(\mathcal{D}^{1,2})^{-1}}, \hbox{ where } 3\leq N\leq 5,$$ which is invalid as $N\geq 6.$ \vskip0.1in \quad In this paper, we prove the quantitative estimate of the Hardy-Littlewood-Sobolev inequality, we get $$d(u)\leq C\|Δu +(I_μ\ast|u|^{2_μ^*})|u|^{2_μ^*-2}u\|_{(\mathcal{D}^{1,2})^{-1}}, \hbox{ when } N=3 \hbox{ and } 5/2< μ<3.$$

math.AP↗