MATH-DT: Scalable Bayesian Online Learning for Digital Twins in Power Network Resilience against Sequential Extreme Events

The objective of this Mathematical Foundations of Digital Twins (MATH-DT) project is to support research on building smarter models of power networks to help them recover more quickly after disasters. Natural hazards like hurricanes and earthquakes often lead to widespread and prolonged power outages. These outages are especially hard to manage when disasters occur in sequence, such as aftershocks or back-to-back storms. This research looks to develop novel tools that enable virtual models — called digital twins — to efficiently learn from data about infrastructure damage and recommend optimal response actions. By combining insights from mathematics and engineering, the project intends to make it possible to simulate and update infrastructure conditions in real time. This new capability can support faster recovery of power systems and improves health, safety, and economic stability. The project also strengthens STEM education through interdisciplinary training in civil engineering and mathematics, hands-on learning for undergraduates, and workshops for utility operators. In addition, it delivers open-source tools that can be reused and enhanced. Power grids are increasingly vulnerable to sequences of extreme events, which complicate recovery and delay service restoration. This project investigates how to improve digital twin systems—virtual models that represent real infrastructure—by advancing three areas of science. First, it develops scalable methods for estimating uncertain and complex infrastructure system behaviors using an ensemble Markov Chain Monte Carlo method. Second, it creates fast physics-based models that simulate how power infrastructure behaves when it is damaged, enabling better decisions about repair. Third, it designs an online learning process that allows these models to update quickly as new data arrives. These contributions seek to advance machine learning, Monte Carlo sampling, stochastic optimization, and numerical linear algebra. Together, they generate a new class of digital twin applications guiding real-time recovery decisions. 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.