Conference: Mathematical Opportunities in Digital Twins (MATH-DT)

在基于物理的建模、数据科学、传感器技术和计算数学方面的最新进展，使得在许多领域产生复杂现实世界系统的“数字孪生”成为可能。这对双胞胎在更好地理解、监控、预测和控制真实世界的系统方面表现出了巨大的希望，特别是在系统的每个方面都不能被观察或建模的情况下。这可以提高安全性、舒适性、维护性，也可以改善人类的健康和福祉。然而，许多根本性的问题和挑战依然存在，特别是关于这一新兴领域的严谨(数学)基础。该奖项为将于2023年12月11日至13日在弗吉尼亚州阿灵顿的乔治梅森大学校园举办的题为“数字双胞胎中的数学机会”的研讨会提供支持。研讨会汇集了在数学、关键应用领域和工业的许多方面工作的主要专家，目的是确定数学可以如何为数字双胞胎的研究做出贡献，以及数字双胞胎如何开辟新的数学方向，以及确定数学界内以及与其他学科的联系、协同作用和组织努力。数字双胞胎可以在许多应用领域带来新的发展，例如：工程，通过确定桥梁、核电站或风力涡轮机等结构中的弱点；医学，器官数字双胞胎可能导致更好的治疗和理解；社会，大型活动的数字双胞胎，如体育游戏，可以提高安全性。会议网站提供了演讲的视频和幻灯片，以及将与整个科学界共享的技术报告，从而促进了会议的广泛影响。学生和早期职业研究人员被邀请参加研讨会，特别关注传统上在STEM中代表性不足的群体。数学模型和计算在模拟、理解和预测物理现象方面一直扮演着重要的角色。虽然传统上，许多模型都是通过严格的数学基础以第一原理为基础的，但这种方法面临着局限性：不是物理系统中的一切都可以使用物理原理来捕获，并且可用的计算资源和算法可能无法对整个复杂系统进行建模，特别是在实时环境中。传感技术的重大进步使具有传感器的复杂现实系统的设备能够使用传感器数据来告知系统的工作情况。此外，数据科学和机器学习的最新发展增强了人们对经验方法的兴趣和信心。然而，纯粹的经验方法没有利用物理原理，可能需要以不可行的成本进行测量和数据生成。本次研讨会的重点是“数字双胞胎”，旨在将基于物理的模型与数据驱动的模型相结合，目标是充分利用这两个领域的优势。数字双胞胎汇聚了数学的几个研究领域(包括：建模、分析、控制、优化、数值分析和科学计算)。这次研讨会有望促进这些重要领域的新发展，并在具有不同数字双胞胎数学背景的研究人员之间启动新的合作，并加强现有的合作。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。

Recent advances in physics-based modeling, data-science, sensor technology, and computational mathematics have made it feasible in many areas to produce a 'Digital Twin' of a complex real world system. Such twins have shown significant promise to better understand, monitor, predict, and control real-world systems, particularly in cases where not every aspect about the system can be observed or modeled. This can improve safety, comfort, maintenance and, also the health and well-being of humans. However, many fundamental questions and challenges remain, particularly regarding a rigorous (mathematical) foundation for this emerging field. This award provides support for a workshop titled “Mathematical Opportunities in Digital Twins” to be held on December 11-13, 2023, in the George Mason University's campus in Arlington, VA. The workshop brings together key experts working in many aspects of mathematics, key application fields, and industry with the goal to determine the ways in which mathematics can contribute to the research on Digital Twins and how Digital Twins can open up new mathematical directions, as well as to identify connections, synergies, and organizational efforts within the mathematical community, and to/with other disciplines. Digital Twins can lead to new developments in many applications, such as: engineering by e.g., determining weaknesses in structures such as bridges, nuclear plants, or wind turbines; medicine, where Digital Twins of organs may lead to better cures and understanding; society, where Digital Twins of large-scale events like sport games can improve safety. A broad impact of the conference is facilitated by the conference website featuring videos and slides of talks and a technical report that will be shared with the entire scientific community. Students and early career researchers are invited to the workshop, with special attention given to groups traditionally underrepresented in STEM. Mathematical models and computations have always played a significant role in simulating, understanding, and predicting physical phenomena. While traditionally, many models have been based on first principles via a rigorous mathematical foundation, such approaches face limitations: Not everything in a physical system can be captured using physical principles, and the available computing resources and algorithms may be unable to model an entire complex system, particularly in real-time environments. Significant advances in sensing technology have enabled the equipment of complex real-world systems with sensors and to employ the sensor data to inform the workings of the system. Moreover, recent developments in data science and machine learning have strengthened the interest and confidence in empirical methodologies. However, purely empirical approaches do not take advantage of the physical principles and may require measurements and data generation at a cost that is not feasible. This workshop focuses on 'Digital Twins', which aim to combine physics-based models with data-driven models, with the goal to leverage the best of both worlds. Digital Twins bring together several research areas in mathematics (including: modeling, analysis, control, optimization, numerical analysis, and scientific computing). This workshop is expected to stimulate new developments in these important areas and to initiate new collaborations, and strengthen the existing ones, among the researchers with diverse background on mathematics of Digital Twins.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.