I am a PhD candidate at Cornell University’s Center for Applied Mathematics, supervised by professor Anil Damle. I work on the design and analysis of numerical methods for data-driven modeling of high-dimensional Earth systems, most often using tools from matrix analysis and numerical linear algebra.

My research develops mathematical theory and numerical methods for synthesizing data-driven and physics-driven approaches to Earth systems modeling. This encompasses methods which use data to improve the forecasts of a physics-driven model (i.e., data assimilation), methods which use a priori physical knowledge to regularize a data-driven model (e.g., structured covariance matrix estimation), and methods for building data-driven models that are physically interpretable (e.g., model order reduction). Because many Earth systems are extremely high-dimensional, computational efficiency is a central concern in my work. In this vein, much of my research has focused on designing and analyzing efficient computational primitives in randomized numerical linear algebra and low-rank approximation.

Starting in August 2026, I will begin postdoctoral studies with professor Melina Freitag at the University of Potsdam Institute for Mathematics. My research there will contribute to the Collaborative Research Centre SFB 1294 on data assimilation.

Publications and Preprints

• R. Armstrong and I. Grooms, “Data Assimilation With An Integral-Form Ensemble Square-Root Filter,” Journal of Computational Physics, 2025, 543, 114413 [JCP online] [arXiv].

• R. Armstrong and A. Damle, “Collect, Commit, Expand: Efficient CPQR-Based Column Selection for Extremely Wide Matrices,” arXiv:2501.18035, 2025 [arXiv] (under review in the SIAM Journal on Scientific Computing).

• R. Armstrong, A. Buzali, and A. Damle, “Structure-Aware Analyses and Algorithms for Interpolative Decompositions,” SIAM Journal on Scientific Computing, 2025, 47 (3), A1527-A1554 [SIAM online] [arXiv].