1405 Soft, Biologically Inspired Numerical Methods to Inverse Problems

Marek Lefik, Lodz University of Technology
Daniela Boso, University of Padova
Tadeusz Burczyński, Polish Academy of Sciences
Some of the most important and well-studied mathematical and physical issues belong to the Inverse Problem (IP) category. They find application in several fields, such as for example: optics, acoustics, geotechnics, medical imaging, signal processing, geophysics, oceanography, astronomy, non-destructive testing and many others.
This minisymposium is focused on the recent progresses in the area of inverse problems, especially as they pertain to soft numerical approaches.
For example, Artificial Neural Networks (ANN) are very natural in solution of inverse problems. Training the network with many sets of causes at the ANN’s output and with the corresponding observable effects at the ANN’s input, one can construct explicitly a numerical approximation to the inverse relation. Such an approximation is well mathematically defined since the ANN can be seen as a universal approximator. Recently, Deep Neural Networks (DNN) and algorithms opened a new chapter in the solution to inverse problems.
In IP solutions, an Evolutionary Algorithm (EA) can also be adopted as the optimizer to search the parameters of the identified system. In this case, the best solution minimises the difference between the observed effect and the response of the identified system. Many efficient EA procedures for the estimation of large numbers of parameters of the identified system have been proposed over the past decades.
Other biologically inspired methods, such as artificial immune systems, swarm optimizers and combined strategies (e.g. an improved simulated annealing combined with EA algorithms; Bayesian approach with ANN, etc.) are particularly interesting in the practice of some important inverse solutions.
One of the main advantages of the discussed methods is that an explicit mathematical formulation of the inverse problem is not necessary, the IP is solved having the formulation of the direct problem only, and by using well known numerical tools developed for forward problems. Furthermore, soft algorithms work relatively well when the inverse problem is ill conditioned.
The presentation of works in diverse fields of inverse problem application is welcome, with a special emphasis on soft, biologically inspired numerical methods. Topics may include, but are not limited to:
• papers presenting applications of soft algorithms to solve inverse problems of different mathematical type;
• various combined strategies basing on classical paradigms of the soft solutions;
• papers discussing robustness, accuracy and efficiency of soft, biologically inspired approach applied to inverse problems;
• papers presenting combination of soft algorithms with various regularization techniques for ill-conditioned inverse problems.