CAREER: Design Under Uncertainty in Combinatorially Expanding Spaces

该学院早期职业发展(CALEAR)奖的目标是开发一个框架，以在小长度尺度上优化设计材料的成分，并进而量化其对零部件性能的影响。工程材料的成分优化对于许多对我们的国家健康、繁荣和福利至关重要的应用是必不可少的。然而，这种类型的设计优化面临着两大挑战，它们极大地降低了设计人员的效率：(1)多个不确定源的共存(例如，缺乏数据、不准确的模拟、未知的参数)；(2)存在既具有分类特征又具有定量特征的巨大的不相交的设计空间。为了解决这些问题并加快设计过程，本项目将把设计问题转化为统计学习问题。这种转换独特地利用了机器学习，使设计人员能够为资源分配、不确定性量化和异常/新颖性检测做出明智的决策。该框架将在复杂浓缩合金的优化设计中展示其影响，这些合金在涉及能量存储、低温操作条件等关键应用中显示出巨大的潜力。该项目的研究成果将与多种教育和推广活动紧密结合，使教育工作者和学生(包括高中和大学)以及企业受益。这些活动将产生教育内容(包括代码和视频教程)和一个用户友好的应用程序，小企业和高中生可以利用它在不确定的情况下进行设计优化。这些活动将向学生和实践者展示工程设计和机器学习可以极大地提高我们解决复杂工程问题的能力。本研究背后的假设是，通过适当的转换算子和学习机制，组合设计空间和相关的不确定性可以通过一组低维和可解释的流形来编码，每个流形都是高维对象(例如不确定性源)的紧凑表示。这一假设将在四个研究项目中得到验证，以做出以下贡献：(1)开发一种不确定性表示方法，提高不确定性量化能力，并为检测模型形式错误和非高斯不确定性的存在提供视觉上可解释的诊断方法；(2)建立一种设计表示方法，用于在紧凑的流形中编码巨大的组合设计空间，设计者可以利用该方法来识别有希望的组合；(3)为概率元建模和资源分配引入新的最优化度量；(4)开发了一个多保真多尺度建模框架，使基于均匀化的多尺度模拟能够动态地、自动地调整嵌套模拟的保真度(从而，成本)和校准参数。这些方法学上的贡献是通用的，可以使广泛的应用受益，例如多学科系统分析。该项目的教育和推广部分包括开发一个可供高中生、教育工作者和当地小企业使用的设计优化和校准应用程序；将材料优化技术转移到制造业；以及开发教育材料和暑期工作坊系列。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The goal of this Faculty Early Career Development (CAREER) award is to develop a framework to optimally design a material’s composition at the small length scales and, in turn, quantify its effects on the component properties. Composition optimization of engineered materials is essential to many applications that are crucial to our national health, prosperity, and welfare. This type of design optimization, however, has two major challenges that dramatically reduce the efficiency of designers: (1) co-existence of multiple uncertainty sources (e.g., lack of data, inaccurate simulations, unknown parameters), and (2) existence of a vast disjoint design space that has both categorical and quantitative features. To address these issues and accelerate the design process, this project will convert the design problem into a statistical learning one. This conversion uniquely leverages machine learning and enables designers to make informed decisions for resource allocation, uncertainty quantification, and anomaly/novelty detection. The impact of the framework will be demonstrated on optimal design of complex concentrated alloys, which have shown great potential in critical applications involving energy storage, cryogenic operating conditions, and more. The research outcomes of this project will be tightly integrated with multiple educational and outreach activities to benefit educators and students (at both high school and university levels), as well as businesses. These activities will produce educational content (including codes and video tutorials) and a user-friendly app that small businesses and high schoolers can leverage for design optimization under uncertainty. These activities will collectively demonstrate to students and practitioners that engineering design and machine learning can dramatically increase our capabilities in solving complex engineering problems.The hypothesis behind this research is that with appropriate conversion operators and learning mechanisms, the combinatorial design space and associated uncertainties can be encoded via a set of low-dimensional and interpretable manifolds, each of which is a compact representation of high-dimensional objects (e.g., an uncertainty source). This hypothesis will be tested in four research thrusts to make the following contributions: (1) Developing an uncertainty representation method that improves uncertainty quantification capabilities and also provides visually interpretable diagnostic measures for detecting model form errors and existence of non-Gaussian uncertainties; (2) Establishing a design representation methodology for encoding a vast combinatorial design space in a compact manifold that designers can leverage to identify promising combinations; (3) Introducing new optimality metrics for probabilistic metamodeling and resource allocation; (4) Developing a multi-fidelity multiscale modeling framework that enables homogenization-based multiscale simulations to dynamically and automatically adjust the fidelity (and hence, cost) and calibration parameters of the nested simulations. These methodological contributions are generic and can benefit a broad range of applications, such as multi-disciplinary systems analysis. The education and outreach components of this project include developing a design optimization and calibration app that can be used by high school students, educators, and local small businesses; transferring the technology on materials optimization to the manufacturing industry; and developing educational materials and summer workshop series.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.