Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

7.6 Numerical Challenges, Distributed Computing and use of Direct or Adjoint Differentiation of Codes

Risk and uncertainty assessments will inevitably lead to a number of runs of the system model that is much larger than for the traditional ‘best-estimate’ study (a single ‘penalised’ calculation). We have seen how, in a strong deterministic paradigm, the maximisation of the response for uncertain areas implies numerous optimisation calculations; in a simple probabilistic paradigm, even with accelerated methods, several dozens or hundreds of calculations are necessary at least. Even if the response surfaces become vital in these last three cases, the following are even greedier (>10³ to 10⁵ calculations):

• the ‘mixed deterministic-probabilistic’ paradigm, which nests a maximisation by intervals for the deterministic components with, for each point, a conditional probabilistic calculation for the probabilised variables;
• optimisation under uncertainty;
• inverse modelling of sources of uncertainty, likewise nesting optimisation and propagation in the general case.

Aside from the optimisation of the code solvers themselves and their parallelisation, the numerical challenge, depending on the propagation methods adopted, can benefit from:

• High Performance Computing (see Chapter 8, Section 8.4), and particularly massive distributed computing, which is immediate in certain methods such as MCS, but which probably requires optimisation for other methods (Berthou et al., 2009).
• The use of ...