Société de Calcul Mathématique, SA




Robust mathematical modeling

 

The Experimental Probabilistic Hypersurface

 

The EPH provides a way of "storing" information, under a probabilistic form : if an experiment, or a computational code, has been executed N times, it provides N results, each depending on the specific values given to the parameters. The EPH gives a way of anticipating, with some probability, a result associated with values of the parameters which have never been met before, or have been lost.

The EPH allows prevision (values in the future) or reconstruction of missing data (values in the past).

In practice, the EPH consists in a collection of densities of probability, one above each point of the configuration space. The density is a Dirac measure (certainty) if the measure has been made at that one point, otherwise, the density is less and less concentrated when we move further away from measure points.

The construction of EPH and its use is the first topic of Olga Zeydina's Ph.D. The general title of this Ph.D. is "Probabilistic Methods for Nuclear Safety". It is prepared at the University of South Britany (Vannes), under the joint supervision of Prof. Emile Le Page (Vannes) and Prof. Bernard Beauzamy (SCM SA).

All documents are in English, pdf format. Click on each link to download the corresponding report.

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  • Practical implementation of the EPH, with VBA code. Random search for dangerous zones, with refined algorithm. In the framework of a contract with IRSN (France), November 2008.

  • Practical implementation of the EPH, with VBA code. Taking into account preliminary information, finding dangerous zones, and so on. In the framework of a contract with IRSN (France), June 2008.

  • An example of the use of EPH for industrial forecast, May 2008.

  • The use of EPH in Epidemiology, as an application of a contract with the CEA, Direction de la Protection et de la Sûreté Nucléaire, March 2008.

  • Comparison of Continuous and Discrete Entropy, by Bernard Beauzamy, October 2007.

  • How to incorporate preliminary information inside the EPH, by Bernard Beauzamy, August 2007.

  • Comments made by S. Destercke, IRSN, following Olga Zeydina's presentation at IRSN/Cadarache, July 2007, and answers by SCM (August 2007).

    Five reports were written during the period 2006-2007, as the result of a contract by the "Institut de Radioprotection et de Sûreté Nucléaire" (IRSN), for the safety of the reactors.

  • Report 5 : Application of the EPH to the location of dangerous zones, May 2007.

  • Report 4 : General Construction and Applications, April 2007. (This is the main document about EPH)

  • Report 3: Explicit Construction from the "Cathare" Code, February 2007.

  • Report 2 : New Construction, January 2007.

  • Report 1 : Practical Construction, December 2006

  • Original construction, by Bernard Beauzamy (for Framatome-ANP), 2004.

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