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During the past decade, many anomaly detection approaches have been introduced in different fields such as network monitoring, fraud detection, and intrusion detection. However, they require understanding of data pattern and often need a long off-line period to build a model or network for the target data. Providing real-time and proactive anomaly detection for streaming time series without human intervention and domain knowledge is highly valuable since it greatly reduces human effort and enables appropriate countermeasures to be undertaken before a disastrous damage, failure, or other harmful event occurs. However, this issue has not been well studied yet. To address it, this paper proposes RePAD, which is a Real-time Proactive Anomaly Detection algorithm for streaming time series based on Long Short-Term Memory (LSTM). RePAD utilizes short-term historic data points to predict and determine whether or not the upcoming data point is a sign that an anomaly is likely to happen in the near future. By dynamically adjusting the detection threshold over time, RePAD is able to tolerate minor pattern change in time series and detect anomalies either proactively or on time. Experiments based on two time series datasets collected from the Numenta Anomaly Benchmark demonstrate that RePAD is able to proactively detect anomalies and provide early warnings in real time without human intervention and domain knowledge.

In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with arbitrary order-of-accuracy and varying degree of implicitness. In this first work, we focus on a new class of implicit-explicit polynomial block methods that are based on fully-implicit Runge-Kutta methods with Radau nodes, and possess high stage order. We show that the new fully-implicit-explicit (FIMEX) integrators have improved stability compared to existing IMEX Runge-Kutta methods, while also being more computationally efficient due to recent developments in preconditioning techniques for solving the associated systems of nonlinear equations. For PDEs on periodic domains where the implicit component is trivial to invert, we will show how parallelization of the right-hand-side evaluations can be exploited to obtain significant speedup compared to existing serial IMEX Runge-Kutta methods. For parallel (in space) finite-element discretizations, the new methods can achieve orders of magnitude better accuracy than existing IMEX Runge-Kutta methods, and/or achieve a given accuracy several times times faster in terms of computational runtime.

In models of opinion dynamics, many parameters -- either in the form of constants or in the form of functions -- play a critical role in describing, calibrating, and forecasting how opinions change with time. When examining a model of opinion dynamics, it is beneficial to infer its parameters using empirical data. In this paper, we study an example of such an inference problem. We consider a mean-field bounded-confidence model with an unknown interaction kernel between individuals. This interaction kernel encodes how individuals with different opinions interact and affect each other's opinions. It is often difficult to quantitatively measure social opinions as empirical data from observations or experiments, so we assume that the available data takes the form of partial observations of the cumulative distribution function of opinions. We prove that certain measurements guarantee a precise and unique inference of the interaction kernel and propose a numerical method to reconstruct an interaction kernel from a limited number of data points. Our numerical results suggest that the error of the inferred interaction kernel decays exponentially as we strategically enlarge the data set.

Network Intrusion and Detection Systems (NIDS) are essential for malicious traffic and cyberattack detection in modern networks. Artificial intelligence-based NIDS are powerful tools that can learn complex data correlations for accurate attack prediction. Graph Neural Networks (GNNs) provide an opportunity to analyze network topology along with flow features which makes them particularly suitable for NIDS applications. However, successful application of such tool requires large amounts of carefully collected and labeled data for training and testing. In this paper we inspect different versions of ToN-IoT dataset and point out inconsistencies in some versions. We filter the full version of ToN-IoT and present a new version labeled ToN-IoT-R. To ensure generalization we propose a new standardized and compact set of flow features which are derived solely from NetFlowv5-compatible data. We separate numeric data and flags into different categories and propose a new dataset-agnostic normalization approach for numeric features. This allows us to preserve meaning of flow flags and we propose to conduct targeted analysis based on, for instance, network protocols. For flow classification we use E-GraphSage algorithm with modified node initialization technique that allows us to add node degree to node features. We achieve high classification accuracy on ToN-IoT-R and compare it with previously published results for ToN-IoT, NF-ToN-IoT, and NF-ToN-IoT-v2. We highlight the importance of careful data collection and labeling and appropriate data preprocessing choice and conclude that the proposed set of features is more applicable for real NIDS due to being less demanding to traffic monitoring equipment while preserving high flow classification accuracy.

Anomaly detection on time series data is increasingly common across various industrial domains that monitor metrics in order to prevent potential accidents and economic losses. However, a scarcity of labeled data and ambiguous definitions of anomalies can complicate these efforts. Recent unsupervised machine learning methods have made remarkable progress in tackling this problem using either single-timestamp predictions or time series reconstructions. While traditionally considered separately, these methods are not mutually exclusive and can offer complementary perspectives on anomaly detection. This paper first highlights the successes and limitations of prediction-based and reconstruction-based methods with visualized time series signals and anomaly scores. We then propose AER (Auto-encoder with Regression), a joint model that combines a vanilla auto-encoder and an LSTM regressor to incorporate the successes and address the limitations of each method. Our model can produce bi-directional predictions while simultaneously reconstructing the original time series by optimizing a joint objective function. Furthermore, we propose several ways of combining the prediction and reconstruction errors through a series of ablation studies. Finally, we compare the performance of the AER architecture against two prediction-based methods and three reconstruction-based methods on 12 well-known univariate time series datasets from NASA, Yahoo, Numenta, and UCR. The results show that AER has the highest averaged F1 score across all datasets (a 23.5% improvement compared to ARIMA) while retaining a runtime similar to its vanilla auto-encoder and regressor components. Our model is available in Orion, an open-source benchmarking tool for time series anomaly detection.

This paper deals with the geometric numerical integration of gradient flow and its application to optimization. Gradient flows often appear as model equations of various physical phenomena, and their dissipation laws are essential. Therefore, dissipative numerical methods, which are numerical methods replicating the dissipation law, have been studied in the literature. Recently, Cheng, Liu, and Shen proposed a novel dissipative method, the Lagrange multiplier approach, for gradient flows, which is computationally cheaper than existing dissipative methods. Although their efficacy is numerically confirmed in existing studies, the existence results of the Lagrange multiplier approach are not known in the literature. In this paper, we establish some existence results. We prove the existence of the solution under a relatively mild assumption. In addition, by restricting ourselves to a special case, we show some existence and uniqueness results with concrete bounds. As gradient flows also appear in optimization, we further apply the latter results to optimization problems.

The aim of this work is to present a parallel solver for a formulation of fluid-structure interaction (FSI) problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The fluid subproblem, consisting of the non-stationary Stokes equations, is discretized in space by $\mathcal{Q}_2$-$\mathcal{P}_1$ finite elements, whereas the structure subproblem, consisting of the linear or finite incompressible elasticity equations, is discretized in space by $\mathcal{Q}_1$ finite elements. A first order semi-implicit finite difference scheme is employed for time discretization. The resulting linear system at each time step is solved by a parallel GMRES solver, accelerated by block diagonal or triangular preconditioners. The parallel implementation is based on the PETSc library. Several numerical tests have been performed on Linux clusters to investigate the effectiveness of the proposed FSI solver.

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

The prevalence of networked sensors and actuators in many real-world systems such as smart buildings, factories, power plants, and data centers generate substantial amounts of multivariate time series data for these systems. The rich sensor data can be continuously monitored for intrusion events through anomaly detection. However, conventional threshold-based anomaly detection methods are inadequate due to the dynamic complexities of these systems, while supervised machine learning methods are unable to exploit the large amounts of data due to the lack of labeled data. On the other hand, current unsupervised machine learning approaches have not fully exploited the spatial-temporal correlation and other dependencies amongst the multiple variables (sensors/actuators) in the system for detecting anomalies. In this work, we propose an unsupervised multivariate anomaly detection method based on Generative Adversarial Networks (GANs). Instead of treating each data stream independently, our proposed MAD-GAN framework considers the entire variable set concurrently to capture the latent interactions amongst the variables. We also fully exploit both the generator and discriminator produced by the GAN, using a novel anomaly score called DR-score to detect anomalies by discrimination and reconstruction. We have tested our proposed MAD-GAN using two recent datasets collected from real-world CPS: the Secure Water Treatment (SWaT) and the Water Distribution (WADI) datasets. Our experimental results showed that the proposed MAD-GAN is effective in reporting anomalies caused by various cyber-intrusions compared in these complex real-world systems.