Data | Bayes | Uncertainty Quantification + Applications

Welcome! I am an interdisciplinary scientist and a physicist by training. The public is paying me to do research, so I thought the public should know what they are paying for. This site is also an invitation to fellow experts to mutually share knowledge and discuss. You can find my research results on this homepage, and a short CV here. After some excursions in propulsion engineering and ultrafast laser spectroscopy in quantum liquids, I came about a topic that has been given at least 5 different names in min. 4 different scientific disciplines:  Probability Theory / Uncertainty Quantification / Statistics / Data Science / Machine Learning. In the same order as above, these disciplines are Physics / Engineering / Mathematics / Computer Science and again Computer Science.  Each discipline has different particular interests, problems and history in this same topic. E.g. in Machine Learning optimization is especially important, in Data Science the data acquisition plays a more prominent role, and Probability Theory seeks a deeper understanding of the foundations. It is clear however that this theme of data analysis and reasoning under uncertainty penetrates through all scientific matters.  In my research, I am particularly interested in the Uncertainty Quantification e.g. of Computer Simulations, as well as Bayesian or Machine Learning approaches. Thus I also draw a lot of resources from the Computational Sciences too.

My tool of choice is Bayesian inference, which I believe to be the most powerful school of scientific reasoning. The Bayesian approach allows to address questions in any of the above mentioned fields and beyond, without having to switch gears, and with only one theoretical framework to be mastered. Curiously enough, this has even been proven mathematically. Read the original proof HERE, or a modernized version in Sivia & Skilling's book "Data Analysis: A Bayesian Tutorial" (Oxford Science Publications 2004). As E.T. Jaynes coined it, Bayesian inference is the logic of science, both fundamental and applied. 

I try to balance fundamental and applied research. Thankfully, within the family of  Bayes and friends there is ample opportunity to do both. Through the Bayesian propositional calculus, the scope of possible research questions is even drastically broader, as any scientific question is formulated in terms of propositions.  Regarding applications, I have a general interest in all kinds of simulations, and a particular interest in biomedical engineering.

Previously I have engaged in the "Lead Project: Mechanics, Modeling and Simulation of Aortic Dissection" (biomechaorta.tugraz.at) with the Institute of Theoretical Physics & Computational Physics (itpcp.tugraz.at) and Graz Center of Computational Engineering (gcce.tugraz.at), where I have completed my PhD studies on "Bayesian Uncertainty Quantification of Numerical Simulations of Aortic Dissection". Aortic Dissection is a disease of the human aorta with a mortality of up to 40 %, and we'd like to change that. My work is at the intersection of probability, machine learning, computational engineering and biomedical engineering.  The stochastic models, numerical simulations and data I am concerned with  stem from biomechanics, impedance cardiography,  computational fluid dynamics, or directly from the clinic. In this endeavour, I have harmonized probability theory and the statistician's approach with the (non-intrusive) engineering approach to uncertainty quantification within a single generalized, coherent Bayesian framework (read the paper HERE). Being rather mathematical, this method enabled us to quantify the blood flow uncertainties in the aorta with computer simulations (read the paper HERE). We also figured out a new method to detect aortic dissections through impedance cardiography (PAPER), now aiming at pre-clinical trials.

Usually there is some known physics e.g. through partial differential equations underlying these problems that could be exploited in the construction of so-called surrogate models.  Thus I have recently also started to work on  Physics-Informed Machine Learning, see e.g. Karniadakis et al. for a great overview. I am using my knowledge of Bayesian probability theory to investigate how to incorporate prior physical information into such learning frameworks. These algorithms in turn are used to solve above mentioned uncertainty quantification problems with improved accuracy, or other computationally expensive problems such as optimization.

I am always happy to collaborate with experts from different fields and curious students, just drop me an e-mail!

SR , 13-01-2022

Key words: Bayesian probability theory, uncertainty quantification, uncertainty propagation, surrogates, meta-models, emulators, statistics, machine learning, data science,  stochastic processes, computer simulations, computational engineering, computational physics, physics-informed machine learning, physics-informed neural networks, physics-constrained machine learning, biomedical engineering, biomechanics, computational fluid dynamics, impedance cardiography, numerical simulations, aortic dissection