Finite difference methods fengshui: alignment through a mathematics of arrays

Numerous scientific-computational domains make use of array data. The core computing of the numerical methods and the algorithms involved is related to multi-dimensional array manipulation. Memory layout and the access patterns of that data are crucial to the optimal performance of the array-based computations. As we move towards exascale computing, writing portable code for efficient data parallel computations is increasingly requiring an abstract productive working environment. To that end, we present the design of a framework for optimizing scientific array-based computations, building a case study for a Partial Differential Equations solver. By embedding the Mathematics of Arrays formalism in the Magnolia programming language, we assemble a software stack capable of abstracting the continuous high-level application layer from the discrete formulation of the collective array-based numerical methods and algorithms and the final detailed low-level code. The case study lays the groundwork for achieving optimized memory layout and efficient computations while preserving a stable abstraction layer independent of underlying algorithms and changes in the architecture.Peer ReviewedPostprint (author's final draft

Tensor Computing for Internet of Things (Dagstuhl Perspectives Workshop 16152)

This report documents the program and the outcomes of Dagstuhl Perspectives Workshop 16152 "Tensor Computing for Internet of Things". In an interactive three-day workshop industrial and academic researchers exchanged their multidisciplinary perspectives through impulse talks, panel discussions, and break-out sessions. Internet of Things (IoT) or Cyber-physical systems (CPS) bring out interesting new challenges to tensor computing, such as the need for real-time analytics and control in interconnected dynamic networks, e.g. electricity, transportation, manufacturing. On the other hand, IoT/CPS have characteristics that make tensor methods applicable to extract information very efficiently. During our discussions we identified an action plan to have a structured approach that will enable the multidisciplinary community of domain and control experts, data scientists, and distributed, embedded software developers to share knowledge and best practices, compare and exchange tensor models depending on data types and applications in distinct IoT/CPS scenarios

Tensor Computing for Internet of Things (Dagstuhl Perspectives Workshop 16152)

"The fundamental laws necessary for the mathematical treatment of large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved." - Dirac 1929 The digital world of Internet of Things (IoT) will provide a high-resolution depiction of our physical world through measurements and other data - even high-definition "video," if you consider streaming data frames coming from a myriad of sensors embedded in everything we use. This depiction will have captured our interactions with the physical world and the interactions of digitally enhanced machines and devices. Tensors, as generalizations of vectors and matrices, provide a natural and scalable framework for handling data with such inherent structures and complex dependencies. Scalable tensor methods have attracted considerable amount of attention, with successes in a series of learning tasks, such as learning latent variable models, relational learning, spatio-temporal forecasting as well as training [19] and compression [20] of deep neural networks. In a Dagstuhl Perspectives Workshop on Tensor Computing for IoT, we validated the fundamental suitability of tensor methods for handling the massive amounts of data coming from connected cyber-physical systems (CPS). The multidisciplinary discourse among academics, industrial researchers and practitioners in the IoT/CPS domain and in the field of machine learning and tensor methods, exposed open issues that need to be addressed to reap value from the technological opportunity. This Manifesto summarizes the immediate action fields for advancement: IoT Tensor Data Benchmarks, Tensor Tools for IoT, and the evolution of a Knowledge Hub. The activities will also be channeled to create best practices and a common tensor language across the disciplines. In a not so distant future, basic infrastructures for living will be mainly data-driven, automated by digitally enhanced devices and machines. The tools and frameworks used to engineer such systems will ensure production-ready machine learning code which utilizes tensor-based, hence better interpretable, models and runs on distributed, decentralized, and embedded computing resources in a robust and reliable way. We conclude the manifesto with a strategy how to move towards this vision with concrete steps in the identified action fields