Introduction to uncertainty quantification (overview)

1. Uncertainty of modeling
Most calculations relies upon more or less uncertain hypothesis about dependable parameters,
initial and boundary values which typically describe geometrical dimensions, as well as physical
parameters such as viscosity. The analysis that propagates these uncertainties to the modeling
result often originates from perspectives and methods of mathematical statistics. The scientific
field Uncertainty Quantification addresses this type of uncertainty of modeling. It is related to but
not equivalent to mathematical statistics, as the latter gathers and infer statistical information of
populations from finite sampling, while the former propagates known statistical information
mathematically. Hence, a statistical analysis of repeated measurements often precedes UQ.
Motivation
The perceived quality, or uncertainty of modeling is of paramount importance for how we use the
result. That is seldom explicitly stated, even though it is always the case. Without trust or
confidence in the result it is literally speaking useless. The perceived quality might however differ
substantially from the true quality – that is why it should be evaluated with credible UQ methods,
rather than vaguely and subjectively guessed from experience.
Modeling uncertainty may be utilized for decision making and risk assessment. For instance,
evaluation of nuclear safety margins, road bridge design and forecasting of critical weather
conditions with ensemble prognosis (Swedish) all rely upon our ability to correctly assess modeling
uncertainty. It may be feasible with experimental verification of bridge strength by pulling and
releasing an attached wire or loading with many heavy trucks. A similar test is not advisable
though for safety critical nuclear applications and is not even possible for particular weather
forecasts. Less critical but nevertheless important applications are development of products like,
e.g. personal cars and heavy vehicles. Typically, a feasibility study suggests three possible versions
and the task is to find 'the best', in order to establish a competitive edge. Simply relying upon
precise numbers obtained from modeling, like fuel consumption, will suggest one only.
Nevertheless, the performance of two versions may be indistinguishable considering the modeling
uncertainty. If so, the result of UQ then suggest an experimental test instead of rejection based on
modeling results. Otherwise, we might accidentally choose the second best version and loose
against competitors which apply UQ more wisely.

2. Our approach
The current prevailing practice is to evaluate modeling uncertainty with a method based on
random sampling. It is also common to ignore the ambiguity implied by the ubiquitous
incompleteness of our knowledge. This gives rise to a whole range of difficulties which
substantially deteriorates the quality of the evaluated uncertainty. Our methodology is different
and to a large extent based on our own research, see list of publications (in this repository). It is
reflected against history and current practice in the strongly simplified illustration ”the right rope”
(in this repository), constructed to be easily understood by anyone.