CAREER: Single-Fidelity vs. Multi-Fidelity Computer Experiments: Unveiling the Effectiveness of Multi-Fidelity Emulation

计算机模型已经成为各个领域不可或缺的工具，使复杂现象的模拟成为可能，并在不需要代价高昂的真实世界实验的情况下促进决策。传统上，计算机模型是使用单一的、高精度的模拟来模拟的，在整个过程中使用高水平的细节和分辨率。然而，最近的进步将注意力转移到了多保真模拟上，通过在模拟中利用不同级别的细节和分辨率来平衡计算成本和精度。一个关键问题出现了：使用单保真和多保真模拟哪个更有效？这是实践者在进行计算机模拟时经常遇到的问题。本研究旨在直接解决这一根本问题，为实际决策提供有价值的见解。通过利用从计算成本比较中获得的见解，这项研究将增强准确预测复杂科学现象的能力，并有可能给工程、医学和生物学等领域带来革命性的变化。该项目有助于推广和多样化努力，激励青年，增加妇女在STEM研究中的代表性。此外，与不同研究小组的合作以及参与REU交流计划，为本科生提供了参与的机会，培养了他们对研究的兴趣，并鼓励他们在STEM追求职业生涯。研究成果将通过出版物和会议传播。开发的代码将被分享，以促进合作，并鼓励其他人在这些创新方法的基础上构建。这项研究通过调查多保真模拟的有效性，解决了进行单保真还是多保真计算机实验的基本问题。它首先检查了两种方法之间的计算成本比较，发现在一定条件下，多保真模拟理论上需要更多的计算资源，同时实现相同的预测能力。为了减少低保真度仿真带来的负面影响，提出了一种新的灵活的统计仿真器--递归非加性(RNA)仿真器来利用多保真度仿真，并基于该仿真器开发了一种序贯设计方案，该仿真器基于平衡不确定性减少和计算成本的准则来选择输入和保真度水平来最大化效率。此外，还开发了两个新的多保真仿真器，称为“安全仿真器”，在理论上保证了与单保真仿真器相比的卓越预测性能，无论设计方案如何。这一奖项反映了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。

Computer models have become indispensable tools across diverse fields, enabling the simulation of complex phenomena and facilitating decision-making without costly real-world experiments. Traditionally, computer models are simulated using single, high-accuracy simulations, employing a high level of detail and resolution throughout. Recent advancements, however, have shifted attention towards multi-fidelity simulations, balancing computational cost and accuracy by leveraging various levels of detail and resolution in the simulation. A key question arises: is it more effective to use single-fidelity or multi-fidelity simulations? This is a question practitioners often confront when conducting computer simulations. The research aims to address this fundamental question directly, providing valuable insights for practical decision-making. By leveraging insights gained from computational cost comparisons, the research will enhance the ability to predict complex scientific phenomena accurately and has the potential to revolutionize fields such as engineering, medical science, and biology. The project contributes to outreach and diversity efforts, inspiring youth and increasing female representation in STEM research. Moreover, collaborations with diverse research groups, as well as involvement in the REU exchange program, provide opportunities to engage undergraduate students, nurturing their interest in research and encouraging them to pursue careers in STEM. Research findings will be disseminated through publications and conferences. The code developed will be shared to foster collaboration and encourage others to build upon these innovative methodologies.This research addresses the fundamental question of whether to conduct single-fidelity or multi-fidelity computer experiments by investigating the effectiveness of multi-fidelity simulations. It begins by examining the computational cost comparison between the two approaches, finding that multi-fidelity simulations, under certain conditions, can theoretically require more computational resources while achieving the same predictive ability. To mitigate the negative effects of low-fidelity simulations, a novel and flexible statistical emulator, called the Recursive Nonadditive (RNA) emulator, is proposed to leverage multi-fidelity simulations, and a sequential design scheme based on this emulator is developed, which maximizes the effectiveness by selecting inputs and fidelity levels based on a criterion that balances uncertainty reduction and computational cost. Furthermore, two novel multi-fidelity emulators, called "secure emulators," are developed, which theoretically guarantee superior predictive performance compared to single-fidelity emulators, regardless of design choices.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.