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.

Publications and Preprints

• R. Armstrong and I. Grooms, “Data Assimilation With An Integral-Form Ensemble Square-Root Filter,” 2025 https://arxiv.org/abs/2503.00253.

• R. Armstrong and A. Damle, “Collect, Commit, Expand: Efficient CPQR-Based Column Selection for Extremely Wide Matrices,” 2025 https://arxiv.org/abs/2501.18035 (submitted to SIAM Journal on Scientific Computing).

• R. Armstrong, A. Buzali, and A. Damle, “Structure-Aware Analyses and Algorithms for Interpolative Decompositions,” 2023 https://arxiv.org/abs/2310.09452 (to appear in SIAM Journal on Scientific Computing).