- Valeriya Naumova, RICAM Linz
- Sergei Pereverzyev, RICAM Linz

"New Trends in Regularization theory and methods for Geomathematical problems"

Geomathematics is a mathematical discipline dedicated to geosciences. It concentrates on the further development of mathematical tools for geosciences such as geodesy, geophysics, seismology, and geoinformatics. Geomathematics is now a growing cross-disciplinary field that engages many mathematicians and geoscientists.

The term “Geomathematics” has only been coined less than two decades ago. It seems that an essential stage was set by the “Handbook of Geomathematics” as a central reference work. Since the summer 2010, Geomathematics sports its own journal “GEM International Journal on Geomathematics.”

Geomathematics primarily aims at helping geoscientists to correctly retrieve physical / chemical / dynamical information on the earth from indirect measurements. Therefore, inverse methods are absolutely essential for mathematical evaluation in these cases. But the point is that there is usually an ill-posed problem in the background of an inverse method, which means that only regularization can make inverse solutions meaningful and useful.

Classical regularization theory is well-known in geosciences community. At the same time, several new and powerful regularization methodologies, such as multi-parameter regularization and regularized data (matrix) completion, have been proposed recently. This new part of regularization theory is now extensively developed towards several applications including machine learning (manifold learning) and medicine (diabetes technology), just to name a few.

Success of newly developed regularization techniques in the above mentioned application areas gives a hope that they may also be profitably used for solving Geomathematical problems. For example, multi-parameter regularization could be useful when a phenomenon of interest is described by several mathematical models simultaneously, which is the case for the use of terrestrial geodata in parallel with space borne ones. As to the regularized data completion, this methodology is of interest for dealing with the polar gap problem, which appears in satellite geodesy due to the fact that the orbit inclination of a satellite leaves the earth's polar areas without data. These are just two examples from the important cooperation area between regularization theory and Geomathematics that could boost the potential of both disciplines.

The main goals of the proposed minisymposium are to set up a new agenda and give a new impulse for such cooperation. To achieve the goals the proposers are going to invite leading experts in both fields to review the state of art and discuss strategy of further development.

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