The Future Directions in Tensor-Based Computation and Modeling

人们认识到，数值多线性代数在科学和工程中发挥着越来越重要的作用。由于存储技术的进步，高维建模已经变得无处不在。面向计算的研究人员不再需要回避涉及庞大的张量结构数据集。为了保持国家在科学计算方面的领导地位，NSF需要审查从基于矩阵的计算思维到基于张量的计算思维的转变，并设计一个协调的计划，以有效地支持这一领域的研究。我们建议举办一个小型的，仅限邀请，为期两天的研讨会，由已建立的研究人员组成，将确定重要的开放问题和机会，发现在计算多线性代数。获得合适的人才组合至关重要，我们计划将关键应用领域的代表与大规模矩阵计算，数值多线性代数，高性能计算，经典数值线性代数以及编程语言领域内的关键领域的专家聚集在一起。根据研讨会上的讨论，将在研讨会一个月后向国家科学基金会提交一份建议文件。

It is recognized that numerical multilinear algebra is playing an increasingly important role across the sciences and engineering. High-dimensional modeling has become ubiquitous because of advances in storage technology. Computatationally-oriented researchers no longer have to be shy about the involvement of unimaginably large, tensor-structured data sets. For the nation to maintain its leadership in scientific computing, the NSF needs to review the progession from matrix-based computational thinking to tensor-based computational thinking and design a coordinated program that will effectively support research in this area. We propose to hold a small, invitation-only, two-day workshop comprised of established researchers that will identify the important open problems and opportunities for discovery in computational multilinear algebra. Getting the right mix of talent is crucial and we plan to assemble representatives from key application areas together with experts in large-scale matrix computations, numerical multilinear algebra, high-performance computing, classical numerical linear algebra, and crucial areas within the field of programming languages. Based on the discussions at the workshop, a document of recommendations will be delivered to the NSF one month after the Workshop.