Overview
My field of expertise lies in high-performance computational mathematics, within the broader, multidisciplinary domain of scientific computing. My work focuses on parameterized partial differential equations (PDEs), which model a wide range of physical phenomena – from wildfire propagation to cardiac electrophysiology. My research objectives, experience, and contributions are centered on advancing state-of-the-art methodologies that address fundamental challenges limiting the scalability, efficiency, and real-world impact of modern scientific computing.
The ever-growing demand for accurate and efficient solutions of parameterized PDEs in real-world scenarios calls for significant advances in computationally efficient surrogate models, particularly those capable of exploiting modern hardware-level parallelism.
To this end, I have specialized in the development of advanced surrogate models for forward and inverse problems governed by parameterized PDEs. My research focuses on the design, implementation, and training of low-dimensional surrogate models – most notably reduced-order models – that incorporate modern techniques from low-rank tensor representations, localization strategies, and message-passing paradigms, enabling scalable performance on distributed-memory supercomputing architectures while remaining compatible with established numerical workflows.
The design and development of extensible, high-performance, and broadly applicable software frameworks for surrogate modeling remains a complex and insufficiently addressed challenge – one in which I have developed substantial expertise. Addressing this problem requires both a deep understanding of the underlying numerical methods (at high and low fidelities) and a principled approach to mathematical software abstraction. These efforts are essential for narrowing the gap between cutting-edge advances in numerical algorithms and their practical deployment in industry and government research environments.
To this end, I have focused on the development of innovative mathematical software design patterns that support the efficient solution of forward and inverse problems involving parameterized PDEs. This includes the implementation of full-order solvers that minimize the cost of high-fidelity computations, as well as the construction of efficient and flexible low-fidelity solvers that integrate seamlessly within multilevel and surrogate-based workflows.
The increasing availability of observational and experimental data, often sparse, noisy, and heterogeneous, poses a fundamental challenge for modern scientific computing: how to systematically integrate data with complex, high-dimensional mathematical models in a way that is both statistically sound and computationally tractable. This challenge is particularly acute for dynamical systems and parameterized PDEs, where uncertainty arises from model error, unknown parameters, incomplete observations, and intrinsic stochasticity.
To this end, I have specialized in the development and analysis of data assimilation and uncertainty quantification techniques for dynamical systems and parameterized PDEs. My work focuses on filtering and Bayesian inference methodologies – such as Kalman-type filters and ensemble-based methods – that enable the principled fusion of model predictions with observational data. A central aspect of this research is the design of scalable algorithms that remain effective in high-dimensional settings, including the use of ensemble methods, reduced-order representations, and localization strategies. These approaches allow uncertainty to be propagated and updated efficiently, bridging the gap between data-driven inference and physics-based modeling in real-world applications.