- Valeriya Naumova, RICAM Linz
- Sergei Pereverzyev, RICAM Linz
"New Trends in Regularization theory and methods for Geomathematical problems"
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.”
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.