Data-driven discovery of governing equations for multidimensional engineering systems

The National Science Foundation Division of Civil, Mechanical, and Manufacturing Innovation awarded South Dakota School of Mines & Technology $473,503 on October 1, 2026, under the Engineering program (CFDA 47.041) to develop mathematical and computational methods for discovering governing equations of multidimensional engineering systems directly from data while preserving spatial and temporal structure.

The award supports research extending sparse identification of nonlinear dynamics methodology to tensor-valued data. Rather than converting multidimensional measurements into long vectors, the approach uses transform-based tensor algebra to decompose large identification problems into smaller, efficiently solvable problems suited to modern computing hardware. The research will establish theoretical recovery guarantees specifying data requirements for accurate system identification. Applications include modeling electric power systems affected by wildfire smoke and other complex spatiotemporal processes.

Deliverables include open-source software, curriculum development, and educational and outreach activities targeting undergraduate and graduate students, teachers, and rural communities through established programs. Period of performance runs from October 1, 2026, through September 30, 2029, with work performed in Rapid City, South Dakota.

Abstract

Modern engineered systems, including electric power grids, environmental monitoring networks, and advanced manufacturing systems, generate large amounts of data that vary across space, time, and multiple physical variables. Understanding the relationships hidden within these data is essential for improving the reliability, efficiency, and resilience of critical infrastructure. Existing data-driven modeling approaches often simplify multidimensional data in ways that lose important structural information, limiting their accuracy, interpretability, and computational efficiency. This award supports research that will create new mathematical and computational methods to discover the underlying behavior of complex engineering systems directly from multidimensional data while preserving its natural spatial and temporal structure. The resulting methods will enable engineers to build more accurate and interpretable models for applications such as electric power systems affected by wildfire smoke and other complex spatiotemporal processes. The project will produce open-source software, educate undergraduate and graduate students, develop instructional materials, and engage teachers and rural communities through established educational and outreach programs. This project develops a new mathematical framework for identifying nonlinear dynamical systems directly from multidimensional data by extending the sparse identification of nonlinear dynamics methodology to tensor-valued data. Rather than converting multidimensional measurements into long vectors, the planned approach preserves their inherent spatial and temporal structure and uses transform-based tensor algebra to decompose a large identification problem into many smaller problems that can be solved efficiently on modern computing hardware. The research establishes theoretical recovery guarantees specifying how much data is required to reliably identify governing equations under this decomposition, extends bayesian statistical methods to quantify uncertainty in the discovered equations, and investigates connections to operator-theoretic approaches for characterizing nonlinear dynamics. The resulting methods will be implemented in open-source software and validated using both benchmark problems and real-world data describing the effects of wildfire smoke on photovoltaic power generation. The project is expected to advance the mathematical foundations of data-driven system identification while providing computationally efficient and interpretable tools for modeling complex spatiotemporal dynamical systems. 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.- subawards are not planned for this award.