“Seht ihr den Mond dort stehen? Er ist nur halb zu sehen, Und ist doch rund und schön! So sind wohl manche Sachen, Die wir getrost belachen, Weil unsre Augen sie nicht sehn.”
The rapidly evolving field of data science recognizes the urgent need for novel computational methods to overcome challenges of parameter inference and uncertainty quantification to ultimately make informed decisions. Emerging fields such as machine learning and uncertainty quantification heavily rely on efficient computational methods for inverse problems.
My research lies within this cross-disciplinary field of inverse problems, which aims at inferring information of physical model giving observations. Techniques developed in this field are of increasing interest to communities such as system biology, systems engineering, and medical and geophysical imaging, to name a few.
The main challenges toward obtaining meaningful real-time solutions to large, data-intensive inverse problems are ill-posedness of the problem, large parameter dimensions, and/or complex model constraints. My research addresses these mathematical, computational, and statistical challenges by exploiting a combination of tools from optimization, dynamical systems, parameter estimation, and optimization, and applied linear algebra. In fact, it is my comprehensive yet broad range of specialties that has enabled me to make significant impacts in the development, analysis, implementation, and validation of new numerical methods and tools for solving inverse problems.
Many of my research projects are crossdisciplinary and driven by applications, with the ultimate goal being a direct transformational impact on fields such as computational biology, geophysical inversion, machine learning, computational ecology, and medical imaging.