Parameters appearing in mathematical models of tumour invasion are
often difficult to assess experimentally and even if experimental
values are available their accuracy might not be very good or they
might have been obtained in a setting different from that what is
modelled. Thus these parameters are uncertain and quantifying the
effect of this uncertainty on the model solution or certain derived
quantities of interest is beneficial for judging the value of the
model and possibly for proposing required dedicated experiments.

We present a framework for uncertainty quantification
based on fast adaptive stochastic collocation on sparse grids. The
advantage of this approach is that it can use an existing simulation
environment for the model under investigation in a black-box fashion.
We apply the framework to a model of tumour invasion and consider
uncertainty in spatially homogeneous as well as heterogeneous
parameters. Spatially heterogeneous parameters represent
random fields and thus are, in general, infinite-dimensional
objects. To make them amenable for a computational analysis, they
first must be approximated by finite dimensional objects. In the case
of correlated random fields, this can be done, for instance, by a
Karhunen-Loève expansion.

Topics covered in this talk also include how uncertainty can be
modelled, how the quantification proceeds, and how certain statistics
of the quantities of interest are computed efficiently.

uncertainty quantification, tumour invasion