NSF Award
2436333
Digital Twins–virtual models of physical systems–have garnered growing attention in recent years, driven by rapid advances in sensing, communications, computing, machine learning and artificial intelligence, and hold the potential to vastly accelerate scientific discovery and revolutionize many industries. In particular, Digital Twins play a fundamental role in designing, managing and optimizing 5G wireless networks and will be essential in enabling next-generation 6G wireless networks. Despite recent advances in realistic channel modeling, there are still many fundamental challenges in developing fit-for-purpose Digital Twins for next generation wireless networks that can seamlessly integrate data for informed decision making, and can be dynamically updated as the physical environment varies and network operational objectives change. Motivated by these challenges, the team of investigators develops novel mathematical theories, and new data-driven, AI-guided models and algorithms that will lay the mathematical foundations for digital twinning of next generation wireless networks. The award also supports undergraduate and graduate students from underrepresented groups in research and educational activities as well as organization of K-12 outreach programs.<br/><br/>This proposal aims to advance the mathematical foundations of next generation wireless network Digital Twins. The investigators will place the ray tracing problem–essential to such digital twins–in the more general framework of first order Hamilton-Jacobi equations, and will make theoretical and algorithmic advances in data-driven learning of Hamilton-Jacobi equations. The research team will prove optimal sample size complexity bounds for learning Hamilton-Jacobi equations and their solutions from data, and develop algorithms for achieving these bounds, in both the static and active learning settings. They will develop a temporal surface reconstruction algorithm that combines temporal LiDAR and video camera information by leveraging neural kernels and transport equations. In order to quantify the uncertainty in their results, the investigators will establish posterior contraction rates for learning Hamilton-Jacobi equations, and develop methods to construct and analyze Bayesian credible sets and perform scalable posterior sampling. Finally, the investigators will integrate their theoretical and algorithmic advances into a next generation wireless network Digital Twin platform that will be evaluated in both controlled and dynamic real-world environments.<br/><br/>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.
