My research centered around computational methods for problems in science and engineering. I am working on a wide range of problems from machine learning to computational electromagnetics. A full list of my publications in google scholar
Machine Learning and Deep Neural Networks
My students and post docs, together with Lars Ruthotto and Eran Triester have been investigating the connections between Ordinary and Partial Differential Equations to Deep Neural Networks. Our first work exploring this connection was published in 2017 and some more recent work can be found here and here.
DNN's can be studied and viewed as a system of time dependent ordinary/partial differential equations. This direction holds promise to many new algorithms to come that will be much more robust and explainable. See my talk here
Visualization of DNN as a dynamical system is demonstrated in this movie
Computational Methods in Electromagnetics Inverse Problems
I have been an Industrial Research Chair in Computational Geoscience developing codes for electromagnetic forward and inverse problems, together with Doug Oldenburg and GIF group. Some of our codes that are geared for researchers are public.The research and matlab codes were published in many papers and in a SIAM book.
In recent years we have been investigating modeling and imaging on a very large scale and using EM techniques in the presence of still casing. See my talk on large scale airborne EM
Finally, collaborating with Computational Geoscience Inc we are exploring real time imaging in a logging while drilling tool.
Medical Image Registration and Optimal Mass Transport
Together with Jan Modersitzki, Lars Ruthotto and Allen Tannenbaum I have been working on medical image registration and optimal mass transport. We have developed a number of computational techniques to obtain better and faster image registration. Some of our recent work can be found on optimal mass transport can be found here