École Nationale Supérieure de
Techniques Avancées

Abstract

Acumen is a hybrid system simulator able to perform rigorous simulations. It uses intervals methods to bound at any time the exact (but unknown) solution. This extension is about supporting a probability distribution on the inputs, and then provides a method to track probabilities to yield a distribution on the output. To do so, a method relying on intervals splitting and P-boxes has been used. It allows to divide the set of initial values into a collection of subsets, each with an associated probability. We show how using this information it is possible to recover a bound on the cumulative density function. The algorithm used to perform this is rigorous but the current implementation includes some non rigorous probability density functions. An additional, orthogonal benefit to introducing splitting is that it provides a robust and standard method to improving the precision of the results of a rigorous simulation. To maintain a strong relation between Acumen’s rigorous and traditional simulators, we also added an interpretation of intervals to the traditional simulator. This support ends up providing a way to do a kind of brute-force Monte-Carlo simulation. The interval splittisng gives some noticeable improvements in precision but the precision of the probability information is very dependant of the system simulated and can go from excellent to very inaccurate. In addition to this, the method needs at least one hundred splits to get an acceptable precision which causes an almost proportional slow-down.