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Hysteresis modeling is crucial to comprehend the behavior of magnetic devices, facilitating optimal designs. Hitherto, deep learning-based methods employed to model hysteresis, face challenges in generalizing to novel input magnetic fields. This paper addresses the generalization challenge by proposing neural operators for modeling constitutive laws that exhibit magnetic hysteresis by learning a mapping between magnetic fields. In particular, three neural operators-deep operator network, Fourier neural operator, and wavelet neural operator-are employed to predict novel first-order reversal curves and minor loops, where novel means they are not used to train the model. In addition, a rate-independent Fourier neural operator is proposed to predict material responses at sampling rates different from those used during training to incorporate the rate-independent characteristics of magnetic hysteresis. The presented numerical experiments demonstrate that neural operators efficiently model magnetic hysteresis, outperforming the traditional neural recurrent methods on various metrics and generalizing to novel magnetic fields. The findings emphasize the advantages of using neural operators for modeling hysteresis under varying magnetic conditions, underscoring their importance in characterizing magnetic material based devices. The codes related to this paper are at github.com/chandratue/magnetic_hysteresis_neural_operator., Comment: 11 pages, 6 figures

Approximation of solutions to partial differential equations (PDE) is an important problem in computational science and engineering. Using neural networks as an ansatz for the solution has proven a challenge in terms of training time and approximation accuracy. In this contribution, we discuss how sampling the hidden weights and biases of the ansatz network from data-agnostic and data-dependent probability distributions allows us to progress on both challenges. In most examples, the random sampling schemes outperform iterative, gradient-based optimization of physics-informed neural networks regarding training time and accuracy by several orders of magnitude. For time-dependent PDE, we construct neural basis functions only in the spatial domain and then solve the associated ordinary differential equation with classical methods from scientific computing over a long time horizon. This alleviates one of the greatest challenges for neural PDE solvers because it does not require us to parameterize the solution in time. For second-order elliptic PDE in Barron spaces, we prove the existence of sampled networks with $L^2$ convergence to the solution. We demonstrate our approach on several time-dependent and static PDEs. We also illustrate how sampled networks can effectively solve inverse problems in this setting. Benefits compared to common numerical schemes include spectral convergence and mesh-free construction of basis functions., Comment: 16 pages, 15 figures

MinMax sampling is a technique for downsampling a real-valued vector which minimizes the maximum variance over all vector components. This approach is useful for reducing the amount of data that must be sent over a constrained network link (e.g. in the wide-area). MinMax can provide unbiased estimates of the vector elements, along with unbiased estimates of aggregates when vectors are combined from multiple locations. In this work, we propose a biased MinMax estimation scheme, B-MinMax, which trades an increase in estimator bias for a reduction in variance. We prove that when no aggregation is performed, B-MinMax obtains a strictly lower MSE compared to the unbiased MinMax estimator. When aggregation is required, B-MinMax is preferable when sample sizes are small or the number of aggregated vectors is limited. Our experiments show that this approach can substantially reduce the MSE for MinMax sampling in many practical settings.

Hysteresis is a ubiquitous phenomenon in science and engineering; its modeling and identification are crucial for understanding and optimizing the behavior of various systems. We develop an ordinary differential equation-based recurrent neural network (RNN) approach to model and quantify the hysteresis, which manifests itself in sequentiality and history-dependence. Our neural oscillator, HystRNN, draws inspiration from coupled-oscillatory RNN and phenomenological hysteresis models to update the hidden states. The performance of HystRNN is evaluated to predict generalized scenarios, involving first-order reversal curves and minor loops. The findings show the ability of HystRNN to generalize its behavior to previously untrained regions, an essential feature that hysteresis models must have. This research highlights the advantage of neural oscillators over the traditional RNN-based methods in capturing complex hysteresis patterns in magnetic materials, where traditional rate-dependent methods are inadequate to capture intrinsic nonlinearity.

A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims to enhance the generalization capabilities of PIML, facilitating practical, real-world applications where accurate predictions in unexplored regions are crucial. We leverage the inherent causality and temporal sequential characteristics of PDE solutions to fuse PIML models with recurrent neural architectures based on systems of ordinary differential equations, referred to as neural oscillators. Through effectively capturing long-time dependencies and mitigating the exploding and vanishing gradient problem, neural oscillators foster improved generalization in PIML tasks. Extensive experimentation involving time-dependent nonlinear PDEs and biharmonic beam equations demonstrates the efficacy of the proposed approach. Incorporating neural oscillators outperforms existing state-of-the-art methods on benchmark problems across various metrics. Consequently, the proposed method improves the generalization capabilities of PIML, providing accurate solutions for extrapolation and prediction beyond the training data., Comment: 13 pages

This article presents an approach for modelling hysteresis in piezoelectric materials, that leverages recent advancements in machine learning, particularly in sparse-regression techniques. While sparse regression has previously been used to model various scientific and engineering phenomena, its application to nonlinear hysteresis modelling in piezoelectric materials has yet to be explored. The study employs the least-squares algorithm with a sequential threshold to model the dynamic system responsible for hysteresis, resulting in a concise model that accurately predicts hysteresis for both simulated and experimental piezoelectric material data. Several numerical experiments are performed, including learning butterfly-shaped hysteresis and modelling real-world hysteresis data for a piezoelectric actuator. The presented approach is compared to traditional regression-based and neural network methods, demonstrating its efficiency and robustness. Source code is available at https://github.com/chandratue/SmartHysteresis

Data stream processing is an increasingly important topic due to the prevalence of smart devices and the demand for real-time analytics. Geo-distributed streaming systems, where cloud-based queries utilize data streams from multiple distributed devices, face challenges since wide-area network (WAN) bandwidth is often scarce or expensive. Edge computing allows us to address these bandwidth costs by utilizing resources close to the devices, e.g. to perform sampling over the incoming data streams, which trades downstream query accuracy to reduce the overall transmission cost. In this paper, we leverage the fact that correlations between data streams may exist across devices located in the same geographical region. Using this insight, we develop a hybrid edge-cloud system which systematically trades off between sampling at the edge and estimation of missing values in the cloud to reduce traffic over the WAN. We present an optimization framework which computes sample sizes at the edge and systematically bounds the number of samples we can estimate in the cloud given the strength of the correlation between streams. Our evaluation with three real-world datasets shows that compared to existing sampling techniques, our system could provide comparable error rates over multiple aggregate queries while reducing WAN traffic by 27-42%., Comment: 12 pages, 11 figures

With the global Internet of Things IoT market size predicted to grow to over 1 trillion dollars in the next 5 years, many large corporations are scrambling to solidify their product line as the defacto device suite for consumers. This has led to each corporation developing their devices in a siloed environment with unique protocols and runtime frameworks that explicitly exclude the ability to work with the competitions devices. This development silo has created problems with programming complexity for application developers as well as concurrency and scalability limitations for applications that involve a network of IoT devices. The Constellation project is a distributed IoT runtime system that attempts to address these challenges by creating an operating system layer that decouples applications from devices. This layer provides mechanisms designed to allow applications to interface with an underlying substrate of IoT devices while abstracting away the complexities of application concurrency, device interoperability, and system scalability. This paper provides an overview of the Constellation system as well as details four new project expansions to improve system scalability., Comment: 15 pages, 11 figures, 2 tables

Edge computing has enabled a large set of emerging edge applications by exploiting data proximity and offloading latency-sensitive and computation-intensive workloads to nearby edge servers. However, supporting edge application users at scale in wide-area environments poses challenges due to limited point-of-presence edge sites and constrained elasticity. In this paper, we introduce Armada: a densely-distributed edge cloud infrastructure that explores the use of dedicated and volunteer resources to serve geo-distributed users in heterogeneous environments. We describe the lightweight Armada architecture and optimization techniques including performance-aware edge selection, auto-scaling and load balancing on the edge, fault tolerance, and in-situ data access. We evaluate Armada in both real-world volunteer environments and emulated platforms to show how common edge applications, namely real-time object detection and face recognition, can be easily deployed on Armada serving distributed users at scale with low latency., Comment: 13 pages, 13 figures

Ever since the commercial offerings of the Cloud started appearing in 2006, the landscape of cloud computing has been undergoing remarkable changes with the emergence of many different types of service offerings, developer productivity enhancement tools, and new application classes as well as the manifestation of cloud functionality closer to the user at the edge. The notion of utility computing, however, has remained constant throughout its evolution, which means that cloud users always seek to save costs of leasing cloud resources while maximizing their use. On the other hand, cloud providers try to maximize their profits while assuring service-level objectives of the cloud-hosted applications and keeping operational costs low. All these outcomes require systematic and sound cloud engineering principles. The aim of this paper is to highlight the importance of cloud engineering, survey the landscape of best practices in cloud engineering and its evolution, discuss many of the existing cloud engineering advances, and identify both the inherent technical challenges and research opportunities for the future of cloud computing in general and cloud engineering in particular., Comment: author copy/preprint of a paper published in the IEEE International Conference on Cloud Engineering (IC2E 2021)

With the rapid growth of large online social networks, the ability to analyze large-scale social structure and behavior has become critically important, and this has led to the development of several scalable graph processing systems. In reality, however, social interaction takes place not only between pairs of individuals as in the graph model, but rather in the context of multi-user groups. Research has shown that such group dynamics can be better modeled through a more general hypergraph model, resulting in the need to build scalable hypergraph processing systems. In this paper, we present MESH, a flexible distributed framework for scalable hypergraph processing. MESH provides an easy-to-use and expressive application programming interface that naturally extends the think like a vertex model common to many popular graph processing systems. Our framework provides a flexible implementation based on an underlying graph processing system, and enables different design choices for the key implementation issues of partitioning a hypergraph representation. We implement MESH on top of the popular GraphX graph processing framework in Apache Spark. Using a variety of real datasets and experiments conducted on a local 8-node cluster as well as a 65-node Amazon AWS testbed, we demonstrate that MESH provides flexibility based on data and application characteristics, as well as scalability with cluster size. We further show that it is competitive in performance to HyperX, another hypergraph processing system based on Spark, while providing a much simpler implementation (requiring about 5X fewer lines of code), thus showing that simplicity and flexibility need not come at the cost of performance., Comment: 14 pages, 15 figures, 2019 IEEE International Conference on Cloud Engineering (IC2E)

Social networks are now ubiquitous and most of them contain interactions involving multiple actors (groups) like author collaborations, teams or emails in an organizations, etc. Hypergraphs are natural structures to effectively capture multi-actor interactions which conventional dyadic graphs fail to capture. In this work the problem of predicting collaborations is addressed while modeling the collaboration network as a hypergraph network. The problem of predicting future multi-actor collaboration is mapped to hyperedge prediction problem. Given that the higher order edge prediction is an inherently hard problem, in this work we restrict to the task of predicting edges (collaborations) that have already been observed in past. In this work, we propose a novel use of hyperincidence temporal tensors to capture time varying hypergraphs and provides a tensor decomposition based prediction algorithm. We quantitatively compare the performance of the hypergraphs based approach with the conventional dyadic graph based approach. Our hypothesis that hypergraphs preserve the information that simple graphs destroy is corroborated by experiments using author collaboration network from the DBLP dataset. Our results demonstrate the strength of hypergraph based approach to predict higher order collaborations (size>4) which is very difficult using dyadic graph based approach. Moreover, while predicting collaborations of size>2 hypergraphs in most cases provide better results with an average increase of approx. 45% in F-Score for different sizes = {3,4,5,6,7}.

MapReduce, the popular programming paradigm for large-scale data processing, has traditionally been deployed over tightly-coupled clusters where the data is already locally available. The assumption that the data and compute resources are available in a single central location, however, no longer holds for many emerging applications in commercial, scientific and social networking domains, where the data is generated in a geographically distributed manner. Further, the computational resources needed for carrying out the data analysis may be distributed across multiple data centers or community resources such as Grids. In this paper, we develop a modeling framework to capture MapReduce execution in a highly distributed environment comprising distributed data sources and distributed computational resources. This framework is flexible enough to capture several design choices and performance optimizations for MapReduce execution. We propose a model-driven optimization that has two key features: (i) it is end-to-end as opposed to myopic optimizations that may only make locally optimal but globally suboptimal decisions, and (ii) it can control multiple MapReduce phases to achieve low runtime, as opposed to single-phase optimizations that may control only individual phases. Our model results show that our optimization can provide nearly 82% and 64% reduction in execution time over myopic and single-phase optimizations, respectively. We have modified Hadoop to implement our model outputs, and using three different MapReduce applications over an 8-node emulated PlanetLab testbed, we show that our optimized Hadoop execution plan achieves 31-41% reduction in runtime over a vanilla Hadoop execution. Our model-driven optimization also provides several insights into the choice of techniques and execution parameters based on application and platform characteristics.

In this paper we investigate a new computing paradigm, called SocialCloud, in which computing nodes are governed by social ties driven from a bootstrapping trust-possessing social graph. We investigate how this paradigm differs from existing computing paradigms, such as grid computing and the conventional cloud computing paradigms. We show that incentives to adopt this paradigm are intuitive and natural, and security and trust guarantees provided by it are solid. We propose metrics for measuring the utility and advantage of this computing paradigm, and using real-world social graphs and structures of social traces; we investigate the potential of this paradigm for ordinary users. We study several design options and trade-offs, such as scheduling algorithms, centralization, and straggler handling, and show how they affect the utility of the paradigm. Interestingly, we conclude that whereas graphs known in the literature for high trust properties do not serve distributed trusted computing algorithms, such as Sybil defenses---for their weak algorithmic properties, such graphs are good candidates for our paradigm for their self-load-balancing features., Comment: 15 pages, 8 figures, 2 tables