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

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.