CAREER: Software Abstractions for Stochastic Embedding in Predictive Simulations on Extreme-Scale Cyberinfrastructure

科学问题的计算机模拟现在被认为是科学探究的第三个支柱，其中基于模拟的预测日益复杂的现实世界问题已经与计算能力的增长相匹配。这些物理问题可以通过包含复杂随机多尺度系统的数学模型来描述。在这样的模型中，一些术语和参数是不确定的，如果在系统级预测中不考虑这些不确定性，可能会导致严重的不准确和无效的预测。为了进行可靠的预测，必须对不确定性进行统计量化，以了解它们对模拟所评估的数量的影响。这种需求导致了一些模拟工具的出现，这些工具已经被应用于解决具有挑战性的问题。然而，这些模拟工具通常以一种特别的方式集成，导致硬件利用率不足，或者就手头的问题而言适用性有限，或者两者兼而有之。因此，需要能够重用现有组件并支持创建新组件的算法和软件元素和抽象，以便它们可以轻松集成以构建用于随机模拟的有效工具。为了实现这一目标，该项目正在研究基于随机嵌入技术的严格和系统方法的新颖抽象。随机嵌入意味着在物理引擎的计算中插入不确定性传播循环/样本。嵌入的思想是为了提高计算效率。通过嵌入，不同的软件组件意识到随机离散化，并且不仅在底层浮点运算中考虑到它，而且在并行化和通信中也考虑到它。这个项目的重点是针对不同物理分析代码的泛化和广泛的随机离散化技术，包括自适应搭配、低秩分离表示和随机伽辽金。最终目标是在下一代计算平台和网络基础设施上实现非常高效和新水平的可靠预测模拟，其中整体随机问题的规模是巨大的（例如，在联合时空随机空间中具有数万亿个自由度）。研究目标是为我们可靠地预测和控制复杂随机多尺度系统的性能提供显著的改进，这反过来将产生巨大的科学，经济和社会影响（例如，使能源生产和管理系统高效可靠）。由此产生的技术有望应用于其他广泛的研究领域，如大规模参数研究、优化和逆问题。该项目建立在一个全面的三管齐下的教育计划之上，包括K-12、本科生和研究生以及更广泛的社区（包括工业界）。其理念是教育和培养下一代研究人员专注于先进的计算和计算科学。这将通过夏令营、课程和讲习班来实现。为了产生最大的影响，本研究的结果将通过各种方法传播，如会议演讲、期刊论文、软件文档和教程。

Computer simulations for scientific problems are now considered as the third pillar of scientific inquiry, where simulation-based prediction for increasingly complex real-world problems has been matched with the growth in computing power. These physical problems can be described mathematically through models that encompass complex stochastic multiscale systems. In such models several terms and parameters are uncertain and not accounting for these uncertainties in the system-level prediction can lead to significant inaccuracies and futile predictions. For reliable predictions, the uncertainties must be statistically quantified to understand their effects on quantities being evaluated by the simulation. This need has given rise to several simulation tools that have been applied to tackle challenging problems. However, these simulation tools are often integrated in an ad-hoc fashion leading to under utilization of the hardware, or limited applicability in terms of the problem at hand, or both. Therefore, algorithmic and software elements and abstractions are needed that can re-use existing components, and support creation of new ones, such that they can be integrated with ease to construct effective tools for stochastic simulations.To achieve this goal, this project is investigating novel abstractions based on a rigorous and systematic approach to stochastic embedding techniques. Stochastic embedding implies insertion of uncertainty propagation loops/samples in the calculations within the physics engine. The idea of embedding is to increase the computational efficiency. With embedding, different software components become aware of the stochastic discretization and account for it not only in the underlying floating-point operations but also in parallelization and communications. The focus of this project is on generalizations that target different physics analysis codes and a broad range of stochastic discretization techniques including adaptive collocation, low-rank separated representation, and stochastic Galerkin. The ultimate goal is to achieve tremendously efficient and new levels of reliable predictive simulations on next-generation computing platforms and cyberinfrastructure, where the size of the overall stochastic problem is enormous (e.g., with many trillions of degrees-of-freedom in the joint spatiotemporal-stochastic space).The research goal is to provide remarkable improvements in our ability to reliably predict and control the performance of complex stochastic multiscale systems, which in-turn will have great scientific, economic and social impacts (e.g., in making energy generation and management systems highly efficient and reliable). The resulting techniques are expected to be applicable to other broad research areas such as large-scale parametric studies, optimization and inverse problems. This project builds on a comprehensive three-pronged education plan that includes K-12, undergraduate and graduate students as well as broader community (including industry). The idea is to educate and grow the next generation of researchers focused on advanced computing and computational science. This will be done through summer camps, courses and workshops. In order to have the maximum impact, results from this research will be disseminated via a variety of methods such as conference presentations, journal papers, software documents, and tutorials.