Search

Unsupervised Domain Adaptation (UDA) has emerged as a key solution in data-driven fault diagnosis, addressing domain shift where models underperform in changing environments. However, under the realm of continually changing environments, UDA tends to underperform on previously seen domains when adapting to new ones - a problem known as catastrophic forgetting. To address this limitation, we introduce the EverAdapt framework, specifically designed for continuous model adaptation in dynamic environments. Central to EverAdapt is a novel Continual Batch Normalization (CBN), which leverages source domain statistics as a reference point to standardize feature representations across domains. EverAdapt not only retains statistical information from previous domains but also adapts effectively to new scenarios. Complementing CBN, we design a class-conditional domain alignment module for effective integration of target domains, and a Sample-efficient Replay strategy to reinforce memory retention. Experiments on real-world datasets demonstrate EverAdapt superiority in maintaining robust fault diagnosis in dynamic environments. Our code is available: https://github.com/mohamedr002/EverAdapt

Background: The use of near-infrared lasers for transcranial photobiomodulation (tPBM) offers a non-invasive method for influencing brain activity and is beneficial for various neurological conditions. Objective: To investigate the safety and neuroprotective properties of tPBM using near-infrared (NIR)-II laser stimulation. Methods: We conducted thirteen experiments involving multidimensional and quantitative methods and measured serum neurobiomarkers, performed electroencephalogram (EEG) and magnetic resonance imaging (MRI) scans, assessed executive functions, and collected a subjective questionnaire. Results: Significant reductions (n=15) in neuron specific enolase (NSE) levels were observed after treatment, indicating neuroprotective effects. No structural or functional brain abnormalities were observed, confirming the safety of tPBM. Additionally, cognitive and executive functions were not impaired, with participants' feedback indicating minimal discomfort. Conclusions: Our data indicate that NIR-II tPBM is safe with specific parameters, highlighting its potential for brain protection.

Applying deep neural networks to 3D point cloud processing has attracted increasing attention due to its advanced performance in many areas, such as AR/VR, autonomous driving, and robotics. However, as neural network models and 3D point clouds expand in size, it becomes a crucial challenge to reduce the computational and memory overhead to meet latency and energy constraints in real-world applications. Although existing approaches have proposed to reduce both computational cost and memory footprint, most of them only address the spatial redundancy in inputs, i.e. removing the redundancy of background points in 3D data. In this paper, we propose a novel post-training weight pruning scheme for 3D object detection that is (1) orthogonal to all existing point cloud sparsifying methods, which determines redundant parameters in the pretrained model that lead to minimal distortion in both locality and confidence (detection distortion); and (2) a universal plug-and-play pruning framework that works with arbitrary 3D detection model. This framework aims to minimize detection distortion of network output to maximally maintain detection precision, by identifying layer-wise sparsity based on second-order Taylor approximation of the distortion. Albeit utilizing second-order information, we introduced a lightweight scheme to efficiently acquire Hessian information, and subsequently perform dynamic programming to solve the layer-wise sparsity. Extensive experiments on KITTI, Nuscenes and ONCE datasets demonstrate that our approach is able to maintain and even boost the detection precision on pruned model under noticeable computation reduction (FLOPs). Noticeably, we achieve over 3.89x, 3.72x FLOPs reduction on CenterPoint and PVRCNN model, respectively, without mAP decrease, significantly improving the state-of-the-art.

Vision transformers have emerged as a promising alternative to convolutional neural networks for various image analysis tasks, offering comparable or superior performance. However, one significant drawback of ViTs is their resource-intensive nature, leading to increased memory footprint, computation complexity, and power consumption. To democratize this high-performance technology and make it more environmentally friendly, it is essential to compress ViT models, reducing their resource requirements while maintaining high performance. In this paper, we introduce a new block-structured pruning to address the resource-intensive issue for ViTs, offering a balanced trade-off between accuracy and hardware acceleration. Unlike unstructured pruning or channel-wise structured pruning, block pruning leverages the block-wise structure of linear layers, resulting in more efficient matrix multiplications. To optimize this pruning scheme, our paper proposes a novel hardware-aware learning objective that simultaneously maximizes speedup and minimizes power consumption during inference, tailored to the block sparsity structure. This objective eliminates the need for empirical look-up tables and focuses solely on reducing parametrized layer connections. Moreover, our paper provides a lightweight algorithm to achieve post-training pruning for ViTs, utilizing second-order Taylor approximation and empirical optimization to solve the proposed hardware-aware objective. Extensive experiments on ImageNet are conducted across various ViT architectures, including DeiT-B and DeiT-S, demonstrating competitive performance with other pruning methods and achieving a remarkable balance between accuracy preservation and power savings. Especially, we achieve up to 3.93x and 1.79x speedups on dedicated hardware and GPUs respectively for DeiT-B, and also observe an inference power reduction by 1.4x on real-world GPUs.

Limited by the scale and diversity of time series data, the neural networks trained on time series data often overfit and show unsatisfacotry performances. In comparison, large language models (LLMs) recently exhibit impressive generalization in diverse fields. Although massive LLM based approaches are proposed for time series tasks, these methods require to load the whole LLM in both training and reference. This high computational demands limit practical applications in resource-constrained settings, like edge-computing and IoT devices. To address this issue, we propose Knowledge Pruning (KP), a novel paradigm for time series learning in this paper. For a specific downstream task, we argue that the world knowledge learned by LLMs is much redundant and only the related knowledge termed as "pertinent knowledge" is useful. Unlike other methods, our KP targets to prune the redundant knowledge and only distill the pertinent knowledge into the target model. This reduces model size and computational costs significantly. Additionally, different from existing LLM based approaches, our KP does not require to load the LLM in the process of training and testing, further easing computational burdens. With our proposed KP, a lightweight network can effectively learn the pertinent knowledge, achieving satisfactory performances with a low computation cost. To verify the effectiveness of our KP, two fundamental tasks on edge-computing devices are investigated in our experiments, where eight diverse environments or benchmarks with different networks are used to verify the generalization of our KP. Through experiments, our KP demonstrates effective learning of pertinent knowledge, achieving notable performance improvements in regression (19.7% on average) and classification (up to 13.7%) tasks, showcasing state-of-the-art results., Comment: 12 pages, 5 figures

Source-free domain adaptation (SFDA) aims to adapt a model pre-trained on a labeled source domain to an unlabeled target domain without access to source data, preserving the source domain's privacy. While SFDA is prevalent in computer vision, it remains largely unexplored in time series analysis. Existing SFDA methods, designed for visual data, struggle to capture the inherent temporal dynamics of time series, hindering adaptation performance. This paper proposes MAsk And imPUte (MAPU), a novel and effective approach for time series SFDA. MAPU addresses the critical challenge of temporal consistency by introducing a novel temporal imputation task. This task involves randomly masking time series signals and leveraging a dedicated temporal imputer to recover the original signal within the learned embedding space, bypassing the complexities of noisy raw data. Notably, MAPU is the first method to explicitly address temporal consistency in the context of time series SFDA. Additionally, it offers seamless integration with existing SFDA methods, providing greater flexibility. We further introduce E-MAPU, which incorporates evidential uncertainty estimation to address the overconfidence issue inherent in softmax predictions. To achieve that, we leverage evidential deep learning to obtain a better-calibrated pre-trained model and adapt the target encoder to map out-of-support target samples to a new feature representation closer to the source domain's support. This fosters better alignment, ultimately enhancing adaptation performance. Extensive experiments on five real-world time series datasets demonstrate that both MAPU and E-MAPU achieve significant performance gains compared to existing methods. These results highlight the effectiveness of our proposed approaches for tackling various time series domain adaptation problems.

In this paper, we construct and analyze new first- and second-order implicit-explicit (IMEX) schemes for the unsteady Navier-Stokes-Darcy model to describe the coupled free flow-porous media system, which is based on the scalar auxiliary variable (SAV) approach in time and finite element method in space. The constructed schemes are linear, only require solving a sequence of linear differential equations with constant coefficients at each time step, and can decouple the Navier-Stokes and Darcy systems. The unconditional stability of both the first- and second-order IMEX schemes can be derived for the coupled system equipped with the Lions interface condition, where the key point is that we should construct a new trilinear form to balance the fully explicit discretizations of the nonlinear terms in the complex system. We can also establish rigorous error estimates for the velocity and hydraulic head of the first-order scheme without any time step restriction. Numerical examples are presented to validate the proposed schemes.

Deep neural networks (DNNs) have been widely used in many artificial intelligence (AI) tasks. However, deploying them brings significant challenges due to the huge cost of memory, energy, and computation. To address these challenges, researchers have developed various model compression techniques such as model quantization and model pruning. Recently, there has been a surge in research of compression methods to achieve model efficiency while retaining the performance. Furthermore, more and more works focus on customizing the DNN hardware accelerators to better leverage the model compression techniques. In addition to efficiency, preserving security and privacy is critical for deploying DNNs. However, the vast and diverse body of related works can be overwhelming. This inspires us to conduct a comprehensive survey on recent research toward the goal of high-performance, cost-efficient, and safe deployment of DNNs. Our survey first covers the mainstream model compression techniques such as model quantization, model pruning, knowledge distillation, and optimizations of non-linear operations. We then introduce recent advances in designing hardware accelerators that can adapt to efficient model compression approaches. Additionally, we discuss how homomorphic encryption can be integrated to secure DNN deployment. Finally, we discuss several issues, such as hardware evaluation, generalization, and integration of various compression approaches. Overall, we aim to provide a big picture of efficient DNNs, from algorithm to hardware accelerators and security perspectives., Comment: This manuscript is the accepted version for TNNLS(IEEE Transactions on Neural Networks and Learning Systems)

We construct new higher-order implicit-explicit (IMEX) schemes using the generalized scalar auxiliary variable (GSAV) approach for the Landau-Lifshitz equation. These schemes are linear, length preserving and only require solving one elliptic equation with constant coefficients at each time step. We show that numerical solutions of these schemes are uniformly bounded without any restriction on the time step size, and establish rigorous error estimates in $l^{\infty}(0,T;H^1(\Omega)) \bigcap l^{2}(0,T;H^2(\Omega))$ of orders 1 to 5 in a unified framework.

Time series data, characterized by its intrinsic long and short-range dependencies, poses a unique challenge across analytical applications. While Transformer-based models excel at capturing long-range dependencies, they face limitations in noise sensitivity, computational efficiency, and overfitting with smaller datasets. In response, we introduce a novel Time Series Lightweight Adaptive Network (TSLANet), as a universal convolutional model for diverse time series tasks. Specifically, we propose an Adaptive Spectral Block, harnessing Fourier analysis to enhance feature representation and to capture both long-term and short-term interactions while mitigating noise via adaptive thresholding. Additionally, we introduce an Interactive Convolution Block and leverage self-supervised learning to refine the capacity of TSLANet for decoding complex temporal patterns and improve its robustness on different datasets. Our comprehensive experiments demonstrate that TSLANet outperforms state-of-the-art models in various tasks spanning classification, forecasting, and anomaly detection, showcasing its resilience and adaptability across a spectrum of noise levels and data sizes. The code is available at https://github.com/emadeldeen24/TSLANet., Comment: Accepted in ICML 2024

This study delves into the potential use of large language models (LLMs) for generating Library of Congress Subject Headings (LCSH). The authors employed ChatGPT to generate subject headings for electronic theses and dissertations (ETDs) based on their titles and abstracts. The results suggests that LLMs such as ChatGPT have the potential to reduce cataloging time needed for assigning LCSH subject terms for ETDs as well as to improve the discovery of this type of resource in academic libraries. Nonetheless, human catalogers remain essential for verifying and enhancing the validity, exhaustivity, and specificity of LCSH generated by LLMs., Comment: 23 pages

Neural Code Intelligence -- leveraging deep learning to understand, generate, and optimize code -- holds immense potential for transformative impacts on the whole society. Bridging the gap between Natural Language and Programming Language, this domain has drawn significant attention from researchers in both research communities over the past few years. This survey presents a systematic and chronological review of the advancements in code intelligence, encompassing over 50 representative models and their variants, more than 20 categories of tasks, and an extensive coverage of over 680 related works. We follow the historical progression to trace the paradigm shifts across different research phases (e.g., from modeling code with recurrent neural networks to the era of Large Language Models). Concurrently, we highlight the major technical transitions in models, tasks, and evaluations spanning through different stages. For applications, we also observe a co-evolving shift. It spans from initial endeavors to tackling specific scenarios, through exploring a diverse array of tasks during its rapid expansion, to currently focusing on tackling increasingly complex and varied real-world challenges. Building on our examination of the developmental trajectories, we further investigate the emerging synergies between code intelligence and broader machine intelligence, uncovering new cross-domain opportunities and illustrating the substantial influence of code intelligence across various domains. Finally, we delve into both the opportunities and challenges associated with this field, alongside elucidating our insights on the most promising research directions. An ongoing, dynamically updated project and resources associated with this survey have been released at https://github.com/QiushiSun/NCISurvey., Comment: 64 pages, 6 figures, 10 tables, 695 references

Sourced from various sensors and organized chronologically, Multivariate Time-Series (MTS) data involves crucial spatial-temporal dependencies, e.g., correlations among sensors. To capture these dependencies, Graph Neural Networks (GNNs) have emerged as powerful tools, yet their effectiveness is restricted by the quality of graph construction from MTS data. Typically, existing approaches construct graphs solely from MTS signals, which may introduce bias due to a small training dataset and may not accurately represent underlying dependencies. To address this challenge, we propose a novel framework named K-Link, leveraging Large Language Models (LLMs) to encode extensive general knowledge and thereby providing effective solutions to reduce the bias. Leveraging the knowledge embedded in LLMs, such as physical principles, we extract a \textit{Knowledge-Link graph}, capturing vast semantic knowledge of sensors and the linkage of the sensor-level knowledge. To harness the potential of the knowledge-link graph in enhancing the graph derived from MTS data, we propose a graph alignment module, facilitating the transfer of semantic knowledge within the knowledge-link graph into the MTS-derived graph. By doing so, we can improve the graph quality, ensuring effective representation learning with GNNs for MTS data. Extensive experiments demonstrate the efficacy of our approach for superior performance across various MTS-related downstream tasks., Comment: 12 pages,7 figures

This work considers a practical semi-supervised graph anomaly detection (GAD) scenario, where part of the nodes in a graph are known to be normal, contrasting to the extensively explored unsupervised setting with a fully unlabeled graph. We reveal that having access to the normal nodes, even just a small percentage of normal nodes, helps enhance the detection performance of existing unsupervised GAD methods when they are adapted to the semi-supervised setting. However, their utilization of these normal nodes is limited. In this paper, we propose a novel Generative GAD approach (namely GGAD) for the semi-supervised scenario to better exploit the normal nodes. The key idea is to generate pseudo anomaly nodes, referred to as 'outlier nodes', for providing effective negative node samples in training a discriminative one-class classifier. The main challenge here lies in the lack of ground truth information about real anomaly nodes. To address this challenge, GGAD is designed to leverage two important priors about the anomaly nodes -- asymmetric local affinity and egocentric closeness -- to generate reliable outlier nodes that assimilate anomaly nodes in both graph structure and feature representations. Comprehensive experiments on six real-world GAD datasets are performed to establish a benchmark for semi-supervised GAD and show that GGAD substantially outperforms state-of-the-art unsupervised and semi-supervised GAD methods with varying numbers of training normal nodes. Code will be made available at https://github.com/mala-lab/GGAD., Comment: 20 pages, 11 figures

In the realm of sequential decision-making tasks, the exploration capability of a reinforcement learning (RL) agent is paramount for achieving high rewards through interactions with the environment. To enhance this crucial ability, we propose SAQN, a novel approach wherein a self-evolving autoencoder (SA) is embedded with a Q-Network (QN). In SAQN, the self-evolving autoencoder architecture adapts and evolves as the agent explores the environment. This evolution enables the autoencoder to capture a diverse range of raw observations and represent them effectively in its latent space. By leveraging the disentangled states extracted from the encoder generated latent space, the QN is trained to determine optimal actions that improve rewards. During the evolution of the autoencoder architecture, a bias-variance regulatory strategy is employed to elicit the optimal response from the RL agent. This strategy involves two key components: (i) fostering the growth of nodes to retain previously acquired knowledge, ensuring a rich representation of the environment, and (ii) pruning the least contributing nodes to maintain a more manageable and tractable latent space. Extensive experimental evaluations conducted on three distinct benchmark environments and a real-world molecular environment demonstrate that the proposed SAQN significantly outperforms state-of-the-art counterparts. The results highlight the effectiveness of the self-evolving autoencoder and its collaboration with the Q-Network in tackling sequential decision-making tasks., Comment: 11 pages, 9 figures, 3 tables

A novel online clustering algorithm is presented where an Evolving Restricted Boltzmann Machine (ERBM) is embedded with a Kohonen Network called ERBM-KNet. The proposed ERBM-KNet efficiently handles streaming data in a single-pass mode using the ERBM, employing a bias-variance strategy for neuron growing and pruning, as well as online clustering based on a cluster update strategy for cluster prediction and cluster center update using KNet. Initially, ERBM evolves its architecture while processing unlabeled image data, effectively disentangling the data distribution in the latent space. Subsequently, the KNet utilizes the feature extracted from ERBM to predict the number of clusters and updates the cluster centers. By overcoming the common challenges associated with clustering algorithms, such as prior initialization of the number of clusters and subpar clustering accuracy, the proposed ERBM-KNet offers significant improvements. Extensive experimental evaluations on four benchmarks and one industry dataset demonstrate the superiority of ERBM-KNet compared to state-of-the-art approaches., Comment: 9 pages, 11 figures, 3 tables

Sparse mixture of experts (SMoE) offers an appealing solution to scale up the model complexity beyond the mean of increasing the network's depth or width. However, effective training of SMoE has proven to be challenging due to the representation collapse issue, which causes parameter redundancy and limited representation potentials. In this work, we propose a competition mechanism to address this fundamental challenge of representation collapse. By routing inputs only to experts with the highest neural response, we show that, under mild assumptions, competition enjoys the same convergence rate as the optimal estimator. We further propose CompeteSMoE, an effective and efficient algorithm to train large language models by deploying a simple router that predicts the competition outcomes. Consequently, CompeteSMoE enjoys strong performance gains from the competition routing policy while having low computation overheads. Our extensive empirical evaluations on two transformer architectures and a wide range of tasks demonstrate the efficacy, robustness, and scalability of CompeteSMoE compared to state-of-the-art SMoE strategies.

By informing the onset of the degradation process, health status evaluation serves as a significant preliminary step for reliable remaining useful life (RUL) estimation of complex equipment. This paper proposes a novel temporal dynamics learning-based model for detecting change points of individual devices, even under variable operating conditions, and utilises the learnt change points to improve the RUL estimation accuracy. During offline model development, the multivariate sensor data are decomposed to learn fused temporal correlation features that are generalisable and representative of normal operation dynamics across multiple operating conditions. Monitoring statistics and control limit thresholds for normal behaviour are dynamically constructed from these learnt temporal features for the unsupervised detection of device-level change points. The detected change points then inform the degradation data labelling for training a long short-term memory (LSTM)-based RUL estimation model. During online monitoring, the temporal correlation dynamics of a query device is monitored for breach of the control limit derived in offline training. If a change point is detected, the device's RUL is estimated with the well-trained offline model for early preventive action. Using C-MAPSS turbofan engines as the case study, the proposed method improved the accuracy by 5.6\% and 7.5\% for two scenarios with six operating conditions, when compared to existing LSTM-based RUL estimation models that do not consider heterogeneous change points., Comment: Accepted in Control Engineering Practice Journal with DOI: https://doi.org/10.1016/j.conengprac.2023.105840

By routing input tokens to only a few split experts, Sparse Mixture-of-Experts has enabled efficient training of large language models. Recent findings suggest that fixing the routers can achieve competitive performance by alleviating the collapsing problem, where all experts eventually learn similar representations. However, this strategy has two key limitations: (i) the policy derived from random routers might be sub-optimal, and (ii) it requires extensive resources during training and evaluation, leading to limited efficiency gains. This work introduces \HyperRout, which dynamically generates the router's parameters through a fixed hypernetwork and trainable embeddings to achieve a balance between training the routers and freezing them to learn an improved routing policy. Extensive experiments across a wide range of tasks demonstrate the superior performance and efficiency gains of \HyperRouter compared to existing routing methods. Our implementation is publicly available at {\url{{https://github.com/giangdip2410/HyperRouter}}}.

Unsupervised Domain Adaptation (UDA) methods have been successful in reducing label dependency by minimizing the domain discrepancy between a labeled source domain and an unlabeled target domain. However, these methods face challenges when dealing with Multivariate Time-Series (MTS) data. MTS data typically consist of multiple sensors, each with its own unique distribution. This characteristic makes it hard to adapt existing UDA methods, which mainly focus on aligning global features while overlooking the distribution discrepancies at the sensor level, to reduce domain discrepancies for MTS data. To address this issue, a practical domain adaptation scenario is formulated as Multivariate Time-Series Unsupervised Domain Adaptation (MTS-UDA). In this paper, we propose SEnsor Alignment (SEA) for MTS-UDA, aiming to reduce domain discrepancy at both the local and global sensor levels. At the local sensor level, we design endo-feature alignment, which aligns sensor features and their correlations across domains. To reduce domain discrepancy at the global sensor level, we design exo-feature alignment that enforces restrictions on global sensor features. We further extend SEA to SEA++ by enhancing the endo-feature alignment. Particularly, we incorporate multi-graph-based high-order alignment for both sensor features and their correlations. Extensive empirical results have demonstrated the state-of-the-art performance of our SEA and SEA++ on public MTS datasets for MTS-UDA.

In this paper we construct new fully decoupled and high-order implicit-explicit (IMEX) schemes for the two-phase incompressible flows based on the new generalized scalar auxiliary variable approach with optimal energy approximation (EOP-GSAV) for Cahn-Hilliard equation and consistent splitting method for Navier-Stokes equation. These schemes are linear, fully decoupled, unconditionally energy stable, only require solving a sequence of elliptic equations with constant coefficients at each time step, and provide a new technique to preserve the consistency between original energy and modified energy. We derive that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. Furthermore, we carry out a rigorous error analysis for the first-order scheme and establish optimal global error estimates for the phase function, velocity and pressure in two and three-dimensional cases. Numerical examples are presented to validate the proposed schemes., Comment: arXiv admin note: text overlap with arXiv:2009.09353

Temporal data, notably time series and spatio-temporal data, are prevalent in real-world applications. They capture dynamic system measurements and are produced in vast quantities by both physical and virtual sensors. Analyzing these data types is vital to harnessing the rich information they encompass and thus benefits a wide range of downstream tasks. Recent advances in large language and other foundational models have spurred increased use of these models in time series and spatio-temporal data mining. Such methodologies not only enable enhanced pattern recognition and reasoning across diverse domains but also lay the groundwork for artificial general intelligence capable of comprehending and processing common temporal data. In this survey, we offer a comprehensive and up-to-date review of large models tailored (or adapted) for time series and spatio-temporal data, spanning four key facets: data types, model categories, model scopes, and application areas/tasks. Our objective is to equip practitioners with the knowledge to develop applications and further research in this underexplored domain. We primarily categorize the existing literature into two major clusters: large models for time series analysis (LM4TS) and spatio-temporal data mining (LM4STD). On this basis, we further classify research based on model scopes (i.e., general vs. domain-specific) and application areas/tasks. We also provide a comprehensive collection of pertinent resources, including datasets, model assets, and useful tools, categorized by mainstream applications. This survey coalesces the latest strides in large model-centric research on time series and spatio-temporal data, underscoring the solid foundations, current advances, practical applications, abundant resources, and future research opportunities., Comment: Ongoing work; 24 pages, 3 figures, 3 tables; Github page: https://github.com/qingsongedu/Awesome-TimeSeries-SpatioTemporal-LM-LLM

While prompt tuning approaches have achieved competitive performance with high efficiency, we observe that they invariably employ the same initialization process, wherein the soft prompt is either randomly initialized or derived from an existing embedding vocabulary. In contrast to these conventional methods, this study aims to investigate an alternative way to derive soft prompt. Our empirical studies show that the soft prompt typically exhibits a low intrinsic rank characteristic. With such observations, we propose decomposed prompt tuning, a novel approach that utilizes low-rank matrices to initialize the soft prompt. Through the low-rank reparameterization, our method significantly reduces the number of trainable parameters while maintaining effectiveness. Experimental results on the SuperGLUE benchmark in both high-resource and low-resource scenarios demonstrate the effectiveness of the proposed method., Comment: Accepted to Findings of EMNLP 2023

The scalar auxiliary variable (SAV)-type methods are very popular techniques for solving various nonlinear dissipative systems. Compared to the semi-implicit method, the baseline SAV method can keep a modified energy dissipation law but doubles the computational cost. The general SAV approach does not add additional computation but needs to solve a semi-implicit solution in advance, which may potentially compromise the accuracy and stability. In this paper, we construct a novel first- and second-order unconditional energy stable and positivity-preserving stabilized SAV (PS-SAV) schemes for $L^2$ and $H^{-1}$ gradient flows. The constructed schemes can reduce nearly half computational cost of the baseline SAV method and preserve its accuracy and stability simultaneously. Meanwhile, the introduced auxiliary variable is always positive while the baseline SAV cannot guarantee this positivity-preserving property. Unconditionally energy dissipation laws are derived for the proposed numerical schemes. We also establish a rigorous error analysis of the first-order scheme for the Allen-Cahn type equation in $l^{\infty}(0,T; H^1(\Omega) ) $ norm. In addition we propose an energy optimization technique to optimize the modified energy close to the original energy. Several interesting numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed methods.

Recently, a new Lagrange multiplier approach was introduced by Cheng, Liu and Shen in \cite{cheng2020new}, which has been broadly used to solve various challenging phase field problems. To design original energy stable schemes, they have to solve a nonlinear algebraic equation to determine the introduced Lagrange multiplier, which can be computationally expensive, especially for large-scale and long-time simulations involving complex nonlinear terms. This paper presents an essential improved technique to modify this issue, which can be seen as a semi-implicit combined Lagrange multiplier approach. In general, the new constructed schemes keep all the advantages of the Lagrange multiplier method and significantly reduce the computation costs. Besides, the new proposed BDF2 scheme dissipates the original energy, as opposed to a modified energy for the classical Lagrange multiplier approach in \cite{cheng2020new}. We further construct high-order BDF$k$ schemes based on the new proposed approach. In addition, we establish a general framework for extending our constructed method to dissipative systems. Finally several examples have been presented to demonstrate the effectiveness of the proposed approach.

Multivariate Time-Series (MTS) data is crucial in various application fields. With its sequential and multi-source (multiple sensors) properties, MTS data inherently exhibits Spatial-Temporal (ST) dependencies, involving temporal correlations between timestamps and spatial correlations between sensors in each timestamp. To effectively leverage this information, Graph Neural Network-based methods (GNNs) have been widely adopted. However, existing approaches separately capture spatial dependency and temporal dependency and fail to capture the correlations between Different sEnsors at Different Timestamps (DEDT). Overlooking such correlations hinders the comprehensive modelling of ST dependencies within MTS data, thus restricting existing GNNs from learning effective representations. To address this limitation, we propose a novel method called Fully-Connected Spatial-Temporal Graph Neural Network (FC-STGNN), including two key components namely FC graph construction and FC graph convolution. For graph construction, we design a decay graph to connect sensors across all timestamps based on their temporal distances, enabling us to fully model the ST dependencies by considering the correlations between DEDT. Further, we devise FC graph convolution with a moving-pooling GNN layer to effectively capture the ST dependencies for learning effective representations. Extensive experiments show the effectiveness of FC-STGNN on multiple MTS datasets compared to SOTA methods. The code is available at https://github.com/Frank-Wang-oss/FCSTGNN., Comment: 10 pages, 8 figures, Accepted by AAAI 2024