CDS&E: ECCS: Accurate and Efficient Uncertainty Quantification and Reliability Assessment for Computational Electromagnetics and Engineering

不确定性量化（UQ）允许对灵敏度和可靠性进行分析，这在所有工程领域都至关重要。事实上，不确定性在所有工程应用中都是不可避免的。仅作为一个示例，生物医学计算电磁学（CEM）应用中的UQ涉及电磁场对场激励器的位置和取向以及生物对象的尺寸和材料的不确定性的灵敏度的研究。通过严格的用户质量，分析和设计的有效性和可靠性可能会大大提高。随着对消费者使用的高精度部件、设备和系统（例如，手机）或国家安全（例如，隐身技术），不确定性分析是极其重要的。事实上，在实际系统和方法的设计中，低概率但高风险的事件往往主导设计关注点。为了实现这些关键目标，该项目将对确定性和统计错误进行连贯的分析和处理，以通过自动和严格的技术来加强工程设计。所提出的CEM和计算工程中的误差控制和UQ方法提高了设计和仿真数据的质量和置信度，同时也提高了效率。虽然该项目侧重于需要高质量严格UQ的安全关键型和任务关键型应用，但所提出的新方法也可以在其他CEM和数值建模应用中提供显着优势。与现有的技术面临的挑战的严重限制的维度不确定的参数空间，计算费用，并能够可靠和准确地建模和计算故障概率，特别是对高风险的事件，所提出的方法具有广泛的适应性，实现高维问题的准确性，并快速计算任意事件的概率。该项目的教育活动包括为研究生提供咨询和培训，从STEM中代表性不足的少数群体中招募学生，开发新的教育和课程材料，以及参与各种保留/推广计划。该项目的主要目标是制定，开发，分析和演示一种新的完全自适应误差控制（确定性和统计性）和不确定性量化的协同方法，以大大提高工程应用（包括电磁系统和设备）可靠性评估的效率，准确性和可用性。该项目开发了一种全面的方法来约束确定性误差（消除重大的误差传播效应）和统计误差（确保高质量的成功和失败概率）。这种新的方法有望大大节省计算资源，并提高高维不确定性的性能。该方法将显着改善安全关键和任务关键问题的分析，要求高质量的用户质量。现有的UQ方法在实际应用中难以对不确定性事件，尤其是低概率高风险事件进行分析。与现有的方法相比，本文提出的新的自适应局部分辨率降维UQ方法具有以下几个独特的特点：（A）与独立的过程相比，全面的确定性和统计误差控制协同作用，有效地驱动局部分辨率增强：（B）在自动UQ过程中对多个目标的整体支持，加速收敛到指定的误差容限;（C）新颖的基于伴随的相似性指示器，以通过兴趣聚类的数量来进行显著的效率增强;（D）对高维不确定性的高弹性，同时支持多个目标并提供显著增强的收敛速率;（E）通过伴随数据指示器和参数敏感性度量的故障概率感知降维技术;以及（F）识别参数空间中的临界点以驱动智能资源分配并识别不稳定区域。总体而言，所提出的方法具有很强的潜力，以满足严格的，自动的，高效的不确定性quantization.This奖项反映了NSF的法定使命的需求，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Uncertainty quantification (UQ) permits analyses of sensitivity and reliability, which is of critical importance in all areas of engineering. Indeed, uncertainty is unavoidable in all engineering applications. Just as one example, UQ in biomedical computational electromagnetics (CEM) applications involves studies of electromagnetic field’s sensitivity to uncertainties in position and orientation of field exciters as well as dimensions and materials of biological objects. Through rigorous UQ, the effectiveness and reliability of analyses and designs may be improved drastically. With the growing demand for high-precision components, devices, and systems for consumer use (e.g., cellphones) or national security (e.g., stealth technology), the analysis of uncertainty is extremely important. In fact, in the design of practical systems and methods, the low-probability but high-risk events often dominate design concerns. To achieve these critical objectives, this project will conduct a cohesive analysis and treatment of deterministic and statistical errors to enhance engineering designs through automatic and rigorous techniques. The proposed methodology for error control and UQ in CEM and computational engineering enhances both quality and confidence in designs and simulation data while also increasing efficiency. Although the project focuses on safety-critical and mission-critical applications requiring high-quality rigorous UQ, the proposed new approach can also provide significant advantages in other CEM and numerical modeling applications. Compared to existing techniques facing challenges of severe limitations in the dimension of uncertain parameter space, the computational expense, and the ability to reliably and accurately model and calculate failure probabilities, particularly for high-risk events, the proposed approach has advantages of extensive adaptivity, achieving accuracy for high-dimensional problems, and computing the probabilities of arbitrary events rapidly. The project’s educational activities include advising and training of graduate students, recruiting students from underrepresented minority groups in STEM, developing new educational and course materials, and participating in various retention/outreach programs. The principal objective of this project is to formulate, develop, analyze, and demonstrate a novel synergistic approach of fully adaptive error control (both deterministic and statistical) and uncertainty quantification to greatly enhance the efficiency, accuracy, and usability of reliability assessment for engineering applications including electromagnetic systems and devices. The project develops a comprehensive approach to constrain deterministic error (to eliminate significant error propagation effects) and statistical error (to ensure high-quality resolution of success and failure probabilities). The novel approach promises significant savings in computational resources and enhanced performance for high-dimensional uncertainty. The approach will significantly improve the analysis of safety-critical and mission-critical problems demanding high-quality UQ. The analysis of uncertain events, particularly those with low-probability and high-risk, is untenable in practical applications through existing UQ approaches. Compared to existing methods, the proposed novel adaptive local resolution with dimension reduction UQ method has several unique features: (A) comprehensive deterministic and statistical error control synergy, as opposed to independent processes, to efficiently drive local resolution enhancements; (B) integral support for multiple objectives in the automated UQ processes with accelerated convergence to specified error tolerances; (C) novel adjoint-based similarity indicators to conduct significant efficiency enhancements through quantity of interest clustering; (D) high-resiliency to high-dimensional uncertainty while supporting multiple objectives and providing significantly enhanced convergence rates; (E) failure-probability-aware dimension reduction techniques through adjoint data indicators and parametric sensitivity metrics; and (F) identification of critical points in the parameter space to drive intelligent resource allocations and identify unstable regions. Overall, the proposed approach has a strong potential to fulfill the needs of rigorous, automatic, and efficient uncertainty quantification.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.