We propose a novel approach that consists in using data mining techniques to perform a sensitivity analysis of approximate models. We give here the example of asymptotic solutions to Vlasov–Maxwell equations, obtained with a paraxial model for relativistic short beams. This new heuristic approach offers new potential applications to treat numerical solutions to mathematical models.
On propose une nouvelle approche mettant en oeuvre des techniques de data mining, pour effectuer une étude de sensiblité de modèles approchées. L'exemple présenté dans cette Note traite d'une approximation paraxiale des équations de Vlasov–Maxwell, valable pour des faisceaux courts relativistes. Cette nouvelle méthodologie ouvre de nouvelles perspectives pour l'analyse d'approximations numériques des modèles mathématiques appliqués aux sciences de l'ingénieur.
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Mots-clés : Informatique, Data mining, Équations de Vlasov–Maxwell
Franck Assous 1, 2; Joel Chaskalovic 1, 3
@article{CRMECA_2010__338_6_305_0, author = {Franck Assous and Joel Chaskalovic}, title = {Data mining techniques for numerical approximations analysis: {A} test case of asymptotic solutions to the {Vlasov{\textendash}Maxwell} equations}, journal = {Comptes Rendus. M\'ecanique}, pages = {305--310}, publisher = {Elsevier}, volume = {338}, number = {6}, year = {2010}, doi = {10.1016/j.crme.2010.07.001}, language = {en}, }
TY - JOUR AU - Franck Assous AU - Joel Chaskalovic TI - Data mining techniques for numerical approximations analysis: A test case of asymptotic solutions to the Vlasov–Maxwell equations JO - Comptes Rendus. Mécanique PY - 2010 SP - 305 EP - 310 VL - 338 IS - 6 PB - Elsevier DO - 10.1016/j.crme.2010.07.001 LA - en ID - CRMECA_2010__338_6_305_0 ER -
%0 Journal Article %A Franck Assous %A Joel Chaskalovic %T Data mining techniques for numerical approximations analysis: A test case of asymptotic solutions to the Vlasov–Maxwell equations %J Comptes Rendus. Mécanique %D 2010 %P 305-310 %V 338 %N 6 %I Elsevier %R 10.1016/j.crme.2010.07.001 %G en %F CRMECA_2010__338_6_305_0
Franck Assous; Joel Chaskalovic. Data mining techniques for numerical approximations analysis: A test case of asymptotic solutions to the Vlasov–Maxwell equations. Comptes Rendus. Mécanique, Volume 338 (2010) no. 6, pp. 305-310. doi : 10.1016/j.crme.2010.07.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.001/
[1] Paraxial approximation of ultrarelativistic intense beams, Numer. Math., Volume 69 (1994) no. 1, pp. 33-60
[2] Numerical paraxial approximation for highly relativistic beams, Comput. Phys. Comm., Volume 180 (2009), pp. 1086-1097
[3] Data Mining with Decision Trees: Theory and Applications, World Scientific Publishing Company, 2001
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