  Modeling biological processes is a highly demanding task because not all
processes are fully understood. Mathematical models allow us to test hypotheses
about possible mechanisms of biological processes. The mathematical mechanisms
oftentimes abstract from the biological micro-scale mechanisms. Experimental
parameter calibration is extremely challenging as the connection between
abstract and micro-scale mechanisms is unknown. Even if some microscopic
parameters can be determined by isolated experiments, the connection to the
abstract mathematical model is challenging. We present ideas for overcoming
these difficulties by using longtime characteristics of solutions for, first,
finding abstract mechanisms covering large-scale observations and, second,
determining parameter values for the abstract mechanisms. The parameter values
are not directly connected to experimental data but serve as a link between
known mechanisms and observations. The framework combines machine learning
techniques with the characteristic solution behavior of differential equations.
This setting gives insight into challenges by using rare data only that can
later be used for partial differential equations.
