To reduce complexity in every simulation or modeling, depending on the matter under study, we strive to exclude any superfluous system data and characteristics. With the enormous, ever-increasing amount of data needing to be processed, the premium is on designing simulations so that they produce the maximum results with a minimum of data and in the shortest possible time. To achieve this objective, using systems analysis we develop methods for model validation and model reduction.
We also focus on technical control aspects in dynamic systems, which include not only the above-mentioned reaction chains in a cell, but also highly automated production flows, for example. Our objective is to design systems with self-correcting feedback mechanisms for optimum operations. The final goal is to do achieve simulations in real-time that will lead to better products and production techniques.
Our work is only feasible if we base it on comprehensive systems analyses and the correct starting parameters. However, the latter cannot always be established by direct measurements. This calls for a mathematical trick, so to speak, that relies on so-called inverse mathematics. Formulating problems with inverse math, equips us to calculate the desired parameters from indirect measurements virtually by working backwards from a certain effect to deduce its cause.
Inverse problems find application in calculating the epicenter of an earthquake, for example, by combining the amplitude of signals from an earthquake sensor and data on geologic conditions.