CAREER: Fast Surrogate Modeling for Design under Uncertainty of Complex Engineering Systems

这项学院早期职业发展(CALEAR)计划拨款将建立一个综合的研究和教育计划，其动机是为复杂工程系统的设计和优化开发基于模拟的预测性方法所带来的挑战。复杂工程系统往往涉及多个尺度上的多种物理现象。例如，在材料和储能系统的设计和制造方面，这类系统主导着当前的工程兴趣。由于材料特性或制造缺陷等原因，这些系统的动力学本质上是可变的，因此迫切需要量化这些不确定性的影响，以便进行准确的性能预测和设计优化。为此，为了推进当前可用于设计和优化的模拟技术，该奖项支持开发一套新的理论、算法和软件工具，用于快速表征和传播不确定性。预测模拟能力在目前和未来的工程系统设计中的重要性和社会影响越来越大，这将成为吸引和吸引未来几代工程师，特别是来自女性和代表不足的少数族裔的工程师进入科罗拉多大学博尔德分校学习的外联和教育工作的基础。不确定性表征和传播的方法是基于新的和可扩展的代理建模方案，以及用于复杂工程系统的稳健设计和优化的有效计算工具。代理建模的思想是构建模型参数和性能目标之间的映射的近似(但评估成本不高)表示。然后，该代理模型用于健壮的设计、优化、敏感性分析或决策。为了能够快速构建代理模型，将在稀疏和低阶近似的背景下开发新的确定性和随机抽样方案以及模型约简方法。新算法的可扩展性的关键是它们有效地自动识别可能存在高维或非光滑系统解的低维流形。代理建模工具将被用于更好地预测锂离子电池单元的可靠性，并促进其电极的不确定性感知设计。

This Faculty Early Career Development (CAREER) Program grant will establish an integrated research and education program motivated by the challenges associated with the development of predictive, simulation-based methods for the design and optimization of complex engineering system. Complex engineering systems often involve multiple physical phenomena at multiple scales. Such systems dominate current engineering interests, for example, as in the design and manufacturing of materials and energy storage systems. The dynamics of these systems are intrinsically variable due to, for instance, material properties or manufacturing imperfections, so that there is an imperative need to quantify the impact of such uncertainties for accurate performance prediction and design optimization. To this end and with the objective of advancing the current simulation technologies available for design and optimization, this award supports the development of a set of novel theories, algorithms, and software tools for fast characterization and propagation of uncertainty. The increasing significance and societal impact of predictive simulation capabilities in present and future design of engineering systems will additionally form the basis of an outreach and education effort to attract and engage future generations of engineers, especially from women and underrepresented minorities, entering and studying at the University of Colorado, Boulder. The approach for uncertainty characterization and propagation is based on new and scalable surrogate modeling 
schemes, together with effective computational tools for robust design and optimization of complex engineering systems. The idea of surrogate modeling is to construct an approximate (but inexpensive to evaluate) representation of the mapping between the parameters of a model and the performance objectives. This surrogate model is then used for robust design, optimization, sensitivity analysis, or decision making. To enable fast construction of surrogate models, novel deterministic and random sampling schemes along with model reduction approaches will be developed, in the context of sparse and low-rank approximations. The key to the scalability of the new algorithms is that they effectively and automatically identify the lower-dimensional manifold on which the possibly high-dimensional or non-smooth system solution exists. The surrogate modeling tools will be employed to better predict the reliability of lithium ion battery cells, and to facilitate the uncertainty-aware design of their electrodes.