Prof. Karen Willcox and I authored a piece for SIAM News about our perspectives and recent work on digital twins. Here is a short excerpt from the article:
"The early successes of digital twin deployment point to the idea’s value and potential impact. Now is the time for the applied mathematics and computational science communities to develop the rigorous mathematical underpinnings and scalable algorithms that will take digital twins to the next level. [For] inspiration we can look to the evolution of the finite element method from an expert-driven approach that required specialization for each different application to a broadly applicable analysis and design tool that is now in the hands of every engineer. This evolution has been enabled by foundational mathematical theory, computing scalability achieved through a combination of hardware and algorithmic advances, and flexible software implementations.
In order to advance digital twins to a similar level of maturity and accessibility, our community’s work in a variety of areas—including physics-based modeling, inverse problems, data assimilation, uncertainty quantification, optimal control, optimal experimental design, surrogate modeling, scientific machine learning, scalable algorithms, and scientific software—has an important role to play."