CAREER: Design Under Uncertainty in Combinatorially Expanding Spaces

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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.