arXiv subjects

Chunyang Wang

Publications and source records attributed to Chunyang Wang.

31 records · Page 2Linked to original sources

arXiv2024

Towards Universal Mesh Movement Networks

Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Ampère PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.

math.NA↗

arXiv2024

Counting random $k$-SAT near the satisfiability threshold

We present efficient counting and sampling algorithms for random $k$-SAT when the clause density satisfies $α\le \frac{2^k}{\mathrm{poly}(k)}.$ In particular, the exponential term $2^k$ matches the satisfiability threshold $Θ(2^k)$ for the existence of a solution and the (conjectured) algorithmic threshold $2^k (\ln k) / k$ for efficiently finding a solution. Previously, the best-known counting and sampling algorithms required far more restricted densities $α\lesssim 2^{k/3}$ [He, Wu, Yang, SODA '23]. Notably, our result goes beyond the lower bound $d\gtrsim 2^{k/2}$ for worst-case $k$-SAT with bounded-degree $d$ [Bezáková et al, SICOMP '19], showing that for counting and sampling, the average-case random $k$-SAT model is computationally much easier than the worst-case model. At the heart of our approach is a new refined analysis of the recent novel coupling procedure by [Wang, Yin, FOCS '24], utilizing the structural properties of random constraint satisfaction problems (CSPs). Crucially, our analysis avoids reliance on the $2$-tree structure used in prior works, which cannot extend beyond the worst-case threshold $2^{k/2}$. Instead, we employ a witness tree similar to that used in the analysis of the Moser-Tardos algorithm [Moser, Tardos, JACM '10] for the Lovász Local lemma, which may be of independent interest. Our new analysis provides a universal framework for efficient counting and sampling for random atomic CSPs, including, for example, random hypergraph colorings. At the same time, it immediately implies as corollaries several structural and probabilistic properties of random CSPs that have been widely studied but rarely justified, including replica symmetry and non-reconstruction.

cs.DS↗

arXiv2024

A Sampling Lovász Local Lemma for Large Domain Sizes

We present polynomial-time algorithms for approximate counting and sampling solutions to constraint satisfaction problems (CSPs) with atomic constraints within the local lemma regime: $$ pD^{2+o_q(1)}\lesssim 1. $$ When the domain size $q$ of each variable becomes sufficiently large, this almost matches the known lower bound $pD^2\gtrsim 1$ for approximate counting and sampling solutions to atomic CSPs [Bezáková et al, SICOMP '19; Galanis, Guo, Wang, TOCT '22], thus establishing an almost tight sampling Lovász local lemma for large domain sizes.

cs.DS↗

arXiv2024

Spatio-Temporal Bi-directional Cross-frame Memory for Distractor Filtering Point Cloud Single Object Tracking

3D single object tracking within LIDAR point clouds is a pivotal task in computer vision, with profound implications for autonomous driving and robotics. However, existing methods, which depend solely on appearance matching via Siamese networks or utilize motion information from successive frames, encounter significant challenges. Issues such as similar objects nearby or occlusions can result in tracker drift. To mitigate these challenges, we design an innovative spatio-temporal bi-directional cross-frame distractor filtering tracker, named STMD-Tracker. Our first step involves the creation of a 4D multi-frame spatio-temporal graph convolution backbone. This design separates KNN graph spatial embedding and incorporates 1D temporal convolution, effectively capturing temporal fluctuations and spatio-temporal information. Subsequently, we devise a novel bi-directional cross-frame memory procedure. This integrates future and synthetic past frame memory to enhance the current memory, thereby improving the accuracy of iteration-based tracking. This iterative memory update mechanism allows our tracker to dynamically compensate for information in the current frame, effectively reducing tracker drift. Lastly, we construct spatially reliable Gaussian masks on the fused features to eliminate distractor points. This is further supplemented by an object-aware sampling strategy, which bolsters the efficiency and precision of object localization, thereby reducing tracking errors caused by distractors. Our extensive experiments on KITTI, NuScenes and Waymo datasets demonstrate that our approach significantly surpasses the current state-of-the-art methods.

cs.CV↗

arXiv2023

Towards derandomising Markov chain Monte Carlo

We present a new framework to derandomise certain Markov chain Monte Carlo (MCMC) algorithms. As in MCMC, we first reduce counting problems to sampling from a sequence of marginal distributions. For the latter task, we introduce a method called coupling towards the past that can, in logarithmic time, evaluate one or a constant number of variables from a stationary Markov chain state. Since there are at most logarithmic random choices, this leads to very simple derandomisation. We provide two applications of this framework, namely efficient deterministic approximate counting algorithms for hypergraph independent sets and hypergraph colourings, under local lemma type conditions matching, up to lower order factors, their state-of-the-art randomised counterparts.

cs.DS↗

arXiv2023

Sampling Lovász Local Lemma For General Constraint Satisfaction Solutions In Near-Linear Time

We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k variables, shares variables with at most $Δ$ constraints, and is violated with probability at most $p$ by a uniform random assignment. The algorithm returns an almost uniform satisfying assignment in expected $\mathrm{poly}(q,k,Δ)\cdot\tilde{O}(n)$ time, as long as a local lemma condition is satisfied: \[ k\cdot p\cdot q^2\cdot Δ^5\le C_0\quad\text{for a suitably small absolute constant }C_0. \] Previously, under similar local lemma conditions, sampling algorithms with running time polynomial in both $n$ and $Δ$ were only known for the almost atomic case, where each constraint is violated by a small number of forbidden local configurations. The key term $Δ^5$ in our local lemma condition also improves the previously best known $Δ^7$ for general CSPs [JPV21b] and $Δ^{5.714}$ for atomic CSPs, including the special case of $k$-CNF [JPV21a, HSW21]. Our sampling approach departs from previous fast algorithms for sampling LLL, which were based on Markov chains. A crucial step of our algorithm is a recursive marginal sampler that is of independent interests. Within a local lemma regime, this marginal sampler can draw a random value for a variable according to its marginal distribution, at a cost independent of the size of the CSP.

cs.DS↗

arXiv2023

PiPAD: Pipelined and Parallel Dynamic GNN Training on GPUs

Dynamic Graph Neural Networks (DGNNs) have been broadly applied in various real-life applications, such as link prediction and pandemic forecast, to capture both static structural information and temporal characteristics from dynamic graphs. Combining both time-dependent and -independent components, DGNNs manifest substantial parallel computation and data reuse potentials, but suffer from severe memory access inefficiency and data transfer overhead under the canonical one-graph-at-a-time training pattern. To tackle the challenges, we propose PiPAD, a $\underline{\textbf{Pi}}pelined$ and $\underline{\textbf{PA}}rallel$ $\underline{\textbf{D}}GNN$ training framework for the end-to-end performance optimization on GPUs. From both the algorithm and runtime level, PiPAD holistically reconstructs the overall training paradigm from the data organization to computation manner. Capable of processing multiple graph snapshots in parallel, PiPAD eliminates the unnecessary data transmission and alleviates memory access inefficiency to improve the overall performance. Our evaluation across various datasets shows PiPAD achieves $1.22\times$-$9.57\times$ speedup over the state-of-the-art DGNN frameworks on three representative models.

cs.LG↗

arXiv2022

Deterministic counting Lovász local lemma beyond linear programming

We give a simple combinatorial algorithm to deterministically approximately count the number of satisfying assignments of general constraint satisfaction problems (CSPs). Suppose that the CSP has domain size $q=O(1)$, each constraint contains at most $k=O(1)$ variables, shares variables with at most $Δ=O(1)$ constraints, and is violated with probability at most $p$ by a uniform random assignment. The algorithm returns in polynomial time in an improved local lemma regime: \[ q^2\cdot k\cdot p\cdotΔ^5\le C_0\quad\text{for a suitably small absolute constant }C_0. \] Here the key term $Δ^5$ improves the previously best known $Δ^7$ for general CSPs [JPV21b] and $Δ^{5.714}$ for the special case of $k$-CNF [JPV21a, HSW21]. Our deterministic counting algorithm is a derandomization of the very recent fast sampling algorithm in [HWY22]. It departs substantially from all previous deterministic counting Lovász local lemma algorithms which relied on linear programming, and gives a deterministic approximate counting algorithm that straightforwardly derandomizes a fast sampling algorithm, hence unifying the fast sampling and deterministic approximate counting in the same algorithmic framework. To obtain the improved regime, in our analysis we develop a refinement of the $\{2,3\}$-trees that were used in the previous analyses of counting/sampling LLL. Similar techniques can be applied to the previous LP-based algorithms to obtain the same improved regime and may be of independent interests.

cs.DS↗

arXiv2022

Incorporating Heterogeneous User Behaviors and Social Influences for Predictive Analysis

Behavior prediction based on historical behavioral data have practical real-world significance. It has been applied in recommendation, predicting academic performance, etc. With the refinement of user data description, the development of new functions, and the fusion of multiple data sources, heterogeneous behavioral data which contain multiple types of behaviors become more and more common. In this paper, we aim to incorporate heterogeneous user behaviors and social influences for behavior predictions. To this end, this paper proposes a variant of Long-Short Term Memory (LSTM) which can consider context information while modeling a behavior sequence, a projection mechanism which can model multi-faceted relationships among different types of behaviors, and a multi-faceted attention mechanism which can dynamically find out informative periods from different facets. Many kinds of behavioral data belong to spatio-temporal data. An unsupervised way to construct a social behavior graph based on spatio-temporal data and to model social influences is proposed. Moreover, a residual learning-based decoder is designed to automatically construct multiple high-order cross features based on social behavior representation and other types of behavior representations. Qualitative and quantitative experiments on real-world datasets have demonstrated the effectiveness of this model.

cs.LG↗

arXiv2022

Deep Meta-learning in Recommendation Systems: A Survey

Deep neural network based recommendation systems have achieved great success as information filtering techniques in recent years. However, since model training from scratch requires sufficient data, deep learning-based recommendation methods still face the bottlenecks of insufficient data and computational inefficiency. Meta-learning, as an emerging paradigm that learns to improve the learning efficiency and generalization ability of algorithms, has shown its strength in tackling the data sparsity issue. Recently, a growing number of studies on deep meta-learning based recommenddation systems have emerged for improving the performance under recommendation scenarios where available data is limited, e.g. user cold-start and item cold-start. Therefore, this survey provides a timely and comprehensive overview of current deep meta-learning based recommendation methods. Specifically, we propose a taxonomy to discuss existing methods according to recommendation scenarios, meta-learning techniques, and meta-knowledge representations, which could provide the design space for meta-learning based recommendation methods. For each recommendation scenario, we further discuss technical details about how existing methods apply meta-learning to improve the generalization ability of recommendation models. Finally, we also point out several limitations in current research and highlight some promising directions for future research in this area.

cs.IR↗

arXiv2021

Bulk High-Entropy Hexaborides

For the first time, a group of CaB6-typed cubic rare earth high-entropy hexaborides have been successfully fabricated into dense bulk pellets (>98.5% in relative densities). The specimens are prepared from elemental precursors via in-situ metal-boron reactive spark plasma sintering. The sintered bulk pellets are determined to be single-phase without any detectable oxides or other secondary phases. The homogenous elemental distributions have been confirmed at both microscale and nanoscale. The Vickers microhardness are measured to be 16-18 GPa at a standard indentation load of 9.8 N. The nanoindentation hardness and Young's moduli have been measured to be 19-22 GPa and 190-250 GPa, respectively, by nanoindentation test using a maximum load of 500 mN. The material work functions are determined to be 3.7-4.0 eV by ultraviolet photoelectron spectroscopy characterizations, which are significantly higher than that of LaB6.

cond-mat.mtrl-sci↗

arXiv2021

TEMImageNet Training Library and AtomSegNet Deep-Learning Models for High-Precision Atom Segmentation, Localization, Denoising, and Super-Resolution Processing of Atomic-Resolution Images

Atom segmentation and localization, noise reduction and deblurring of atomic-resolution scanning transmission electron microscopy (STEM) images with high precision and robustness is a challenging task. Although several conventional algorithms, such has thresholding, edge detection and clustering, can achieve reasonable performance in some predefined sceneries, they tend to fail when interferences from the background are strong and unpredictable. Particularly, for atomic-resolution STEM images, so far there is no well-established algorithm that is robust enough to segment or detect all atomic columns when there is large thickness variation in a recorded image. Herein, we report the development of a training library and a deep learning method that can perform robust and precise atom segmentation, localization, denoising, and super-resolution processing of experimental images. Despite using simulated images as training datasets, the deep-learning model can self-adapt to experimental STEM images and shows outstanding performance in atom detection and localization in challenging contrast conditions and the precision consistently outperforms the state-of-the-art two-dimensional Gaussian fit method. Taking a step further, we have deployed our deep-learning models to a desktop app with a graphical user interface and the app is free and open-source. We have also built a TEM ImageNet project website for easy browsing and downloading of the training data.

cond-mat.mtrl-sci↗

arXiv2020

0.71-Å resolution electron tomography enabled by deep learning aided information recovery

Electron tomography, as an important 3D imaging method, offers a powerful method to probe the 3D structure of materials from the nano- to the atomic-scale. However, as a grant challenge, radiation intolerance of the nanoscale samples and the missing-wedge-induced information loss and artifacts greatly hindered us from obtaining 3D atomic structures with high fidelity. Here, for the first time, by combining generative adversarial models with state-of-the-art network architectures, we demonstrate the resolution of electron tomography can be improved to 0.71 angstrom which is the highest three-dimensional imaging resolution that has been reported thus far. We also show it is possible to recover the lost information and remove artifacts in the reconstructed tomograms by only acquiring data from -50 to +50 degrees (44% reduction of dosage compared to -90 to +90 degrees full tilt series). In contrast to conventional methods, the deep learning model shows outstanding performance for both macroscopic objects and atomic features solving the long-standing dosage and missing-wedge problems in electron tomography. Our work provides important guidance for the application of machine learning methods to tomographic imaging and sheds light on its applications in other 3D imaging techniques.

cond-mat.mtrl-sci↗