Machine learning for simulation-based model approximation

Prof. Dr. Bernard Haasdonk

Daniel Wirtz

This project considers model reduction of parametric, nonlinear dynamical systems and combines different techniques known from the classical model reduction with methods of machine learning.

The past few years show that simulations enjoy a growing interest in research and development. The steady increase in computational resources allows the simulation and evaluation of more complex and more computationally expensive models. Nevertheless, the high fidelity or high resolution require in many contexts solutions of very high-dimensional, nonlinear models that might in addition be time- and parameter-dependent.
If such models are used for optimization, statistical analysis or control, the total computation time grows too large to be economically feasible - even with high performance computers.
Thus, model reduction techniques are inevitable for large simulation models in order to drastically reduce the computing time while the results are of similar quality as the original model.

In particular, the reduction is simulation-based in this project, i.e. nonlinear approximations and optimal parameter spaces are computed based on single, selected simulations.
The method is applied to a variety of different dynamical systems from the field of fluid dynamics, biochemistry and (bio-)mechanics.

Within the scope of this project, several cooperations with co-workers of other institutes emerged.
There is a collaboration with S. Waldherr (IST) regarding the biochemistry simulations with the chemical master
equation. The collaboration with M. Daub (IADM) is continued and problems concerning the reduction that emerged in 2011 are further researched.

The multidisciplinary SimTech seminar for model reduction, that already existed before the project was started, was successfully continued in 2011.

The collaboration with N. Karajan (Inst. Appl. Mech.) in the field of simulations for the spine and spinal disks is continued with the application described above.

While the person in charge of the project attended the PhD course of the Ferienakademie Munich/Stuttgart/Erlangen, another cooperation with C. Strohmeyer (Dept. Math. MSO) of the University of Erlangen emerged.
Within this cooperation, the capability of reduction techniques for simulations of piping systems (as illustrated above) is investigated. The elaborator of the project D. Wirtz was invited to Erlangen as guest researcher within the scope of this project to elaborate the different possibilities of a collaboration more closely.