Research

Accelerated Numerical Methods

Accelerated numerical techniques for discrete inverse problems often center on developing efficient iterative methods utilizing strategies such as mixed-to-low precision computing, randomization, and optimized data movement in memory. Low-to-mixed precision shows particular promise in preconditioning, where, because inverse problems have limits on achievable solution quality under realistic noise, computing low-rank Kronecker product preconditioners in low precision for iterative solvers like LSQR can achieve significant speedups without loss of accuracy. The unifying goal across these themes is the development of precision and communication aware iterative solvers for inverse problems that are robust, efficient, and architecture conscious.

Model and Data-driven Applications

Mathematically grounded models play a central role in connecting computational inverse problems to real world impact. Applications such as weather forecasting, pollutant surveillance, and image-guided surgery require time-critical reconstructions, where solutions must be accurate, computationally efficient, and aligned with domain-specific constraints. These challenges demand methods that are both data-aware and model-driven, leveraging interdisciplinary collaboration to design algorithms that improve progressively as data arrives. 

Multi-linear Algebraic Representations

Data is often naturally represented as multiway arrays or tensors, and as a result, tensor-based approaches have revolutionized feature extraction and compression. As a newly recent focus of research for me - this research focuses on understanding and developing algorithms that can harness matrix-mimetic tensor frameworks that preserve desirable linear algebraic properties (think rank, orthogonality, and multiplication). The ultimate goal of this thrust is to develop scalable inverse problem solution strategies using multi-linear (tensor) computational frameworks.