Research

Frequentist confidence intervals for ill-posed inverse problems:

Introduced a new framework for frequentist, optimization-based intervals that provably achieve desired coverage in ill-posed inverse problems without introducing a prior distribution [AoS, under revision]. The framework unifies many previously proposed optimization-based intervals and disproves a conjecture dating back to 1965. Explored sampling techniques based on the frameworks, with applications in particle physics problems and satellite data from NASA Jet Propulsion Laboratory (preprint in progress).

Game-theoretical Uncertainty Quantification:

Introduced the concept of data-likelihood constraints in the two-player zero-sum game setting of Wald, which makes solving the game computationally tractable and helps navigate the inherent accuracy-robustness tradeoff of statistical inference [JCP]. The output of the algorithm is a robust estimate and a certificate of worst-case optimality. Applied the framework earthquake number prediction in the Groningen region in the Netherlands, introducing the notion of aleatoric and epistemic uncertainty to the field [Seismological Research Letters].

Gaussian Processes for scientific computing and inference:

Developed methods for learning and solving PDEs [JCP, under review], Opeator Learning [JCP], and Measure Transport [SIMODS, under review], showing in all cases that Gaussian Processes lead to algorithms with stronger convergence guarantees than every other Machine Learning method without sacrificing accuracy. Also used GP-based methods to encode information-theoretic information in RNA classification application [Physica D]

Gaussian Processes for computational graph discovery:

Introduced a method to discover the structure of computational graphs using the variance decomposition properties of Gaussian Processes [PNAS]. We apply this to chemistry and biology examples, and to control of a lunar rover through an ongoing collaboration with NASA JPL.

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