RANDOMNESS: A RESOURCE FOR REAL-TIME ANALYTICS

适用范围：现代工程依靠数据和模型，通过预测和诊断分析来扩大我们对复杂系统、设备和过程的理解。这方面的例子包括用于能量转换的流体动力学模拟、用于地球物理和环境监测的电磁模型、用于弹性基础设施设计的力学、用于无损检测的声学和x射线模型以及用于生物医学成像的光学模型。传统上，数值计算一直处于工程的前沿，但其在工程过程中的嵌入仍然受到与实际数据模型相关的复杂性的阻碍。目前，过程分析要么离线操作，在高性能计算基础设施上进行精确的模拟和复杂的数据处理算法，要么基于产生一些粗糙的命令信息的过于简化的问题规范进行实时操作。挑战：为了在制造和质量保证过程中通过实时、准确的建模和数据处理来增强以数据为中心的工程能力，我们接受了实时、大规模计算的挑战，用更有效的随机方案取代了我们执行代数计算的传统方式。以线性方程的基本解为例，该方法随机选取矩阵和向量中的一小部分元素，从根本上减少了计算量和时间。更令人印象深刻的是，当最佳采样时，这种计算效率也得到了非常小的解决方案误差的补充，因此，通过研究我们可以计算这些最佳采样分布的方法，我们可以实现大量的计算节省，最终为经济的生产部门提供一个负担得起的实时建模和数据处理解决方案，而不会影响所寻求信息的质量和准确性。主要目标：这个项目的主要目标是通过结合随机线性代数的算法来开发一种新的流行的有限元方法。通过理论、分析和计算，我们试图证明随机有限元法的概念，通过研究如何以有效的方式计算和采样各自的最佳抽样分布，来模拟扩散过程和解决相关的反数据拟合问题。为什么这很重要？该项目的成功将为广泛的工程和制造部门提供精确、便携和负担得起的高维计算做出可衡量的贡献，即使在高性能计算基础设施不可用的情况下，也可以实现实时过程监控和控制。它会带来什么不同？我们新颖的数据分析框架旨在为复杂和动态的数据和模型提供及时和准确的见解。在制造过程中，这将导致生产率的提高，服务和产品质量的监控，以及运营成本和浪费的减少。我们还预见到，这些进步将在更广泛的工程领域得到应用，并对健康信息学产生影响，使癌症患者和国家安全能够同时成像和治疗，从而能够实时检测和筛选线程。

The scope: Modern engineering relies on data and models to broaden our understanding of complex systems, devices and processes, through predictive and diagnostic analytics. Examples of this include fluid dynamic simulations for energy conversion, electromagnetic models in geophysical and environmental monitoring, mechanics in design of resilient infrastructures, acoustic and X-ray models for non-destructive testing and optical models in biomedical imaging. Traditionally, numerical computing has been at the forefront of engineering, however its embedding within the engineering process is still hindered by the complexity associated with realistic data models. Currently, process analytics, operate either off-line, on high performance computing infrastructure for accurate simulations and sophisticated data processing algorithms, or in real-timebased on oversimplified problem specifications that yield some crude imperative information.The challenge:To empower data centric engineering in manufacturing and quality assurance processes with real-time, accurate modelling and data processing we take on the challenge of real-time, large-scale computing, by replacing the conventional way we perform algebraic computations with a more efficient randomised scheme. In the context of basic solution of linear equations for example, this approach randomly selects a small fraction of the elements in the matrices and the vectors involved, radically reducing the computational effort and time. What's more impressive than this, is that when optimally sampled, this computational efficiency is also complemented by a very small solution error, and thus by investigating ways that we can compute these optimal sampling distributions we can achieve massive computational savings, ultimately providing the productive sectors of the economy with an affordable solution for real-time modelling and data processing, without compromising the quality and accuracy of the sought information.Main objectives:The main objective of this project is to develop a new form of the popular finite element method by incorporating algorithms for randomised linear algebra. Through theory, analysis and computation we seek to prove a concept of randomised finite element method for simulating diffusion processes and solving the associated inverse data-fitting problems by investigating how the respective optimal sampling distributions can be computed and sampled in an efficient way.Why does it matter?The success of this project will make a measurable contribution on making accurate, high-dimensional computing portable and affordable to the broad engineering and manufacturing sector, allowing for real-time process monitoring and control even where high performance computing infrastructure is not available.What difference will it achieve?Our novel framework of data analytics aims to provide prompt and accurate insights into complex and dynamic data and models. In a manufacturing process this will lead to a rise in productivity, monitoring quality of services and products, as well as reduction of operational costs and waste. We also foresee that these advances will find application in the broader engineering sector as well as having an impact health informatics to enable simultaneous imaging and therapy for cancer patients and national security in being able to detect and screen in real time against threads.