A new error analysis for parabolic Dirichlet boundary control problems

In this paper, we consider the finite element approximation to a parabolic Dirichlet boundary control problem and establish new a priori error estimates. In the temporal semi-discretization we apply the DG(0) method for the state and the variational discretization for the control, and obtain the convergence rates $O(k^{\frac{1}{4}})$ and $O(k^{\frac{3}{4}-\varepsilon})$ $(\varepsilon>0)$ for the control for problems posed on polytopes with $y_0\in L^2(\Omega)$, $y_d\in L^2(I;L^2(\Omega))$ and smooth domains with $y_0\in H^{\frac{1}{2}}(\Omega)$, $y_d\in L^2(I;H^1(\Omega))\cap H^{\frac{1}{2}}(I;L^2(\Omega))$, respectively. In the fully discretization of the optimal control problem posed on polytopal domains, we apply the DG(0)-CG(1) method for the state and the variational discretization approach for the control, and derive the convergence order $O(k^{\frac{1}{4}} +h^{\frac{1}{2}})$, which improves the known results by removing the mesh size condition $k=O(h^2)$ between the space mesh size $h$ and the time step $k$. As a byproduct, we obtain a priori error estimate $O(h+k^{1\over 2})$ for the fully discretization of parabolic equations with inhomogeneous Dirichlet data posed on polytopes, which also improves the known error estimate by removing the above mesh size condition

Trust Region Methods For Nonconvex Stochastic Optimization Beyond Lipschitz Smoothness

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular significance within the realms of deep neural networks and distributionally robust optimization (DRO). We demonstrate the significant advantage of trust region methods for stochastic nonconvex optimization under such generalized smoothness assumption. We show that first-order trust region methods can recover the normalized and clipped stochastic gradient as special cases and then provide a unified analysis to show their convergence to first-order stationary conditions. Motivated by the important application of DRO, we propose a generalized high-order smoothness condition, under which second-order trust region methods can achieve a complexity of $\mathcal{O}(\epsilon^{-3.5})$ for convergence to second-order stationary points. By incorporating variance reduction, the second-order trust region method obtains an even better complexity of $\mathcal{O}(\epsilon^{-3})$, matching the optimal bound for standard smooth optimization. To our best knowledge, this is the first work to show convergence beyond the first-order stationary condition for generalized smooth optimization. Preliminary experiments show that our proposed algorithms perform favorably compared with existing methods

Contribution of anthropogenic activities to the intensification of heat index-based spatiotemporally contiguous heatwave events in China

In this study, we identified heat index (HI)-based spatiotemporally contiguous heatwaves (HI-STHWs) in China based on meteorological observations and CMIP6 global climate model simulations. We analyzed the spatiotemporal patterns of changes in HI-STHWs in the past and future and quantitatively attributed these changes to anthropogenic activities. The results show that the duration, severity, average, maximum, and total impacted area of the annual strongest HI-STHWs during the present period of 1991–2014 are 1.77, 2.0, 1.05, 1.14, and 1.89 times the historical period of 1961–1990, respectively. In the fingerprint results, the anthropogenic greenhouse gases (GHG) signal is significantly detected, while the aerosol (AER) and natural (NAT) signals are not. GHG is the primary factor driving the intensification of HI-STHWs, which alone explains about 130%, 122%, 112%, 111%, and 114% of the above changes. The reason for GHG contribution exceeding 100% is that AER might have a negative contribution although nonsignificant. In the future warming climate, anthropogenic activities are projected to lead to more unprecedented HI-STHWs. Under the high emissions scenario of SSP585, by 2100, the annual strongest HI-STHW in China is projected to last almost the whole year and influence 96% regions of China in the most serious day. Meanwhile, its duration and total impacted area are 24.5 [17.2, 31.6] (90% confidence interval) and 107.2 [70, 129.9] times the preindustrial period. However, if the warming level could be limited to 2/1.5 °C, those values would be 3.4/5.4 and 8.2/16.2 times smaller than that under the SSP585 scenario by 2100

TOE: A Grid-Tagging Discontinuous NER Model Enhanced by Embedding Tag/Word Relations and More Fine-Grained Tags

So far, discontinuous named entity recognition (NER) has received increasing research attention and many related methods have surged such as hypergraph-based methods, span-based methods, and sequence-to-sequence (Seq2Seq) methods, etc. However, these methods more or less suffer from some problems such as decoding ambiguity and efficiency, which limit their performance. Recently, grid-tagging methods, which benefit from the flexible design of tagging systems and model architectures, have shown superiority to adapt for various information extraction tasks. In this paper, we follow the line of such methods and propose a competitive grid-tagging model for discontinuous NER. We call our model TOE because we incorporate two kinds of Tag-Oriented Enhancement mechanisms into a state-of-the-art (SOTA) grid-tagging model that casts the NER problem into word-word relationship prediction. First, we design a Tag Representation Embedding Module (TREM) to force our model to consider not only word-word relationships but also word-tag and tag-tag relationships. Concretely, we construct tag representations and embed them into TREM, so that TREM can treat tag and word representations as queries/keys/values and utilize self-attention to model their relationships. On the other hand, motivated by the Next-Neighboring-Word (NNW) and Tail-Head-Word (THW) tags in the SOTA model, we add two new symmetric tags, namely Previous-Neighboring-Word (PNW) and Head-Tail-Word (HTW), to model more fine-grained word-word relationships and alleviate error propagation from tag prediction. In the experiments of three benchmark datasets, namely CADEC, ShARe13 and ShARe14, our TOE model pushes the SOTA results by about 0.83%, 0.05% and 0.66% in F1, demonstrating its effectiveness

Industry 4.0-Oriented Turnkey Project: Rapid Configuration and Intelligent Operation of Manufacturing Systems

More extensive personalized product requirements and shorter product life cycles have put forward higher requirements for the rapid establishment, commissioning, and operation of corresponding manufacturing systems. However, the traditional manufacturing system development process is complicated, resulting in a longer delivery time. Many manufacturing enterprises, especially small and micro enterprises, may not have the necessary manufacturing knowledge or capabilities to meet these requirements. Therefore, it is essential to promote the construction of turnkey projects under the paradigm of Industry 4.0, parallelizing and integrating the existing manufacturing system development process based on mass manufacturing equipment to quickly provide turnkey solutions for manufacturing systems’ configuration and implementation for these enterprises. This paper aims to extract and refine the configuration and operation key views of the Industry 4.0-oriented Turnkey Project (I4TP) from Reference Architecture Model Industrie 4.0 (RAMI4.0) and use it to guide the development of key functional processes of turnkey projects to achieve rapid configuration and efficient operation management of manufacturing systems. The turnkey project platform in the Advanced Manufacturing Technology Center (AMTC) is taken as a demonstration case to provide a reference idea for the rapid configuration and intelligent operation of the turnkey manufacturing system

A narrow-band parameterization for the stochastic gravitational wave background

In light of the non-perturbative resonance effects that may occur during inflation, we introduce a parametrization for the power spectrum of the stochastic gravitational wave background (SGWB) characterized by narrow-band amplification. We utilize the universal $\Omega_\text{GW}\propto k^3$ infrared limit, applicable to a wide array of gravitational wave sources, to devise a robust yet straightforward parameterization optimized for Markov Chain Monte Carlo (MCMC) analyses. This parameterization is demonstrated through select examples where its application is pertinent, and we discuss the advantages of this approach over traditional parametrizations for narrow-band scenarios. To evaluate the sensitivity of our proposed model parameters, we apply a mock likelihood based on the CMB-Stage4 data. Furthermore, we explicate the computational process for the mapping relationship between the foundational model parameters and our parameterized framework, using a two-field inflation model that resonantly amplifies gravitational waves (GWs) as an example

Video-Bench: A Comprehensive Benchmark and Toolkit for Evaluating Video-based Large Language Models

Video-based large language models (Video-LLMs) have been recently introduced, targeting both fundamental improvements in perception and comprehension, and a diverse range of user inquiries. In pursuit of the ultimate goal of achieving artificial general intelligence, a truly intelligent Video-LLM model should not only see and understand the surroundings, but also possess human-level commonsense, and make well-informed decisions for the users. To guide the development of such a model, the establishment of a robust and comprehensive evaluation system becomes crucial. To this end, this paper proposes \textit{Video-Bench}, a new comprehensive benchmark along with a toolkit specifically designed for evaluating Video-LLMs. The benchmark comprises 10 meticulously crafted tasks, evaluating the capabilities of Video-LLMs across three distinct levels: Video-exclusive Understanding, Prior Knowledge-based Question-Answering, and Comprehension and Decision-making. In addition, we introduce an automatic toolkit tailored to process model outputs for various tasks, facilitating the calculation of metrics and generating convenient final scores. We evaluate 8 representative Video-LLMs using \textit{Video-Bench}. The findings reveal that current Video-LLMs still fall considerably short of achieving human-like comprehension and analysis of real-world videos, offering valuable insights for future research directions. The benchmark and toolkit are available at: \url{https://github.com/PKU-YuanGroup/Video-Bench}.Comment: Benchmark is available at https://github.com/PKU-YuanGroup/Video-Benc

MADAv2: Advanced Multi-Anchor Based Active Domain Adaptation Segmentation

Unsupervised domain adaption has been widely adopted in tasks with scarce annotated data. Unfortunately, mapping the target-domain distribution to the source-domain unconditionally may distort the essential structural information of the target-domain data, leading to inferior performance. To address this issue, we firstly propose to introduce active sample selection to assist domain adaptation regarding the semantic segmentation task. By innovatively adopting multiple anchors instead of a single centroid, both source and target domains can be better characterized as multimodal distributions, in which way more complementary and informative samples are selected from the target domain. With only a little workload to manually annotate these active samples, the distortion of the target-domain distribution can be effectively alleviated, achieving a large performance gain. In addition, a powerful semi-supervised domain adaptation strategy is proposed to alleviate the long-tail distribution problem and further improve the segmentation performance. Extensive experiments are conducted on public datasets, and the results demonstrate that the proposed approach outperforms state-of-the-art methods by large margins and achieves similar performance to the fully-supervised upperbound, i.e., 71.4% mIoU on GTA5 and 71.8% mIoU on SYNTHIA. The effectiveness of each component is also verified by thorough ablation studies.Comment: Accepted by TPAMI-IEEE Transactions on Pattern Analysis and Machine Intelligence. arXiv admin note: substantial text overlap with arXiv:2108.0801

Tiny Multi-Agent DRL for Twins Migration in UAV Metaverses: A Multi-Leader Multi-Follower Stackelberg Game Approach

The synergy between Unmanned Aerial Vehicles (UAVs) and metaverses is giving rise to an emerging paradigm named UAV metaverses, which create a unified ecosystem that blends physical and virtual spaces, transforming drone interaction and virtual exploration. UAV Twins (UTs), as the digital twins of UAVs that revolutionize UAV applications by making them more immersive, realistic, and informative, are deployed and updated on ground base stations, e.g., RoadSide Units (RSUs), to offer metaverse services for UAV Metaverse Users (UMUs). Due to the dynamic mobility of UAVs and limited communication coverages of RSUs, it is essential to perform real-time UT migration to ensure seamless immersive experiences for UMUs. However, selecting appropriate RSUs and optimizing the required bandwidth is challenging for achieving reliable and efficient UT migration. To address the challenges, we propose a tiny machine learning-based Stackelberg game framework based on pruning techniques for efficient UT migration in UAV metaverses. Specifically, we formulate a multi-leader multi-follower Stackelberg model considering a new immersion metric of UMUs in the utilities of UAVs. Then, we design a Tiny Multi-Agent Deep Reinforcement Learning (Tiny MADRL) algorithm to obtain the tiny networks representing the optimal game solution. Specifically, the actor-critic network leverages the pruning techniques to reduce the number of network parameters and achieve model size and computation reduction, allowing for efficient implementation of Tiny MADRL. Numerical results demonstrate that our proposed schemes have better performance than traditional schemes

Mechanical Enhancement of Fractured Laminated Glass considering Fragment Overlaps and Temperatures

The post-fracture performance of laminated glass is becoming a significant focus due to the growing breakage incidents of tempered glass and its long-term replacement. However, the influence of tension stiffening due to the adhesion of glass fragments to polymeric interlayers, one of the main factors affecting the structural capacity of the post-fracture laminated glass, is still unclear, especially when considering different fragment overlaps and temperatures. In this work, two types of uniaxial tensile tests with predefined cracks, including the multiple through-cracked tensile (MTCT) and the multiple offset-cracked tensile (MOCT), were conducted at 20, 50, and 80℃. Both PVB and SG were considered. Additionally, the influence of the overlap length of offset fragments and initial delamination on tension stiffening was investigated based on finite element models. The results show that the mechanical properties of the composite materials, which correspond to a local response in the post-fracture laminated glass, are strongly dependent on the fragment overlap, temperature, and interfacial delamination. Moreover, the influence of the fragment overlap on the mechanical enhancement becomes pronounced even at high temperatures, which should be taken into account for the evaluation of the post-fracture performance of laminated glass