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

8.4 The Promise of High Performance Computing

8.4.1 The Computational Load of Risk and Uncertainty Modelling

Risk and uncertainty studies lead inevitably to a number of calls to the code for the phenomenological system models that is much larger than for the traditional ‘best-estimate’ study (a single ‘penalised’ calculation). Before adding the optimisation layer of this chapter, standard probabilistic uncertainty propagation involves at least several dozen or hundreds of calculations even when using the accelerated methods reviewed in Chapter 7, and much more when considering the robust computation of low-probability risk measures. Table 8.6 provides some orders of magnitude of the increase multiple in the computational budget with respect to a traditional engineering computation that does not represent uncertainty while already representing a large CPU cost because of the size of meshes and complexity of phenomenological equations.

Table 8.6 Computing challenges: number of code runs per type of analysis.

Task	Number of code runs	Comments
Risk computation – uncertainty propagation
Level 1 – EZ, Var Z	N = 101 −102
Level 1 – quantile zα or P(Z > zs)	N = 101p (or 102) to >104 according to α	Linearly increases with 1/(1-α) for robust methods (indep. of p), or less quickly for accelerated ones (+linear with p)
Level 2	N = 101−102p	As an additional factor multiplying the level-1 increase multiple
Importance ranking – sensitivity analysis
For var Z	N = 3p to >103