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              <p>Uncertainty quantification in computational physics requires running many simulations. For some industrial applications, the complexity of the numerical model is incompatible with the number of simulations to be run. Solving physics equations in a reduced computation time is therefore essential for the design of safe and reliable systems. In this thesis, we propose a new numerical method combining model order reduction and machine learning to compute an approximate solution of a stochastic partial differential equation in a reasonable computation time. With this method, the mechanical behavior of an aircraft engine’s component is predicted 636 times faster than with the original high-fidelity model with less than 3% of errors, which enables quantifying the uncertainties generated by the thermal loading.</p>
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              <p>La quantification d’incertitudes dans les simulations numériques requiert de lancer un grand nombre de calculs. Pour certaines applications industrielles, la complexité des modèles physiques utilisés est incompatible avec le nombre de simulations requises. Accélérer la résolution d’équations décrivant un problème physique donné est essentiel dans l’optique de concevoir des systèmes fiables et sûrs. Dans cette thèse, nous proposons une nouvelle méthode combinant la réduction de modèle et l’apprentissage statistique pour prédire rapidement une solution approchée d’une équation aux dérivées partielles stochastique. Le comportement mécanique d’une pièce d’un turboréacteur a ainsi pu être calculé 636 fois plus vite qu’avec le modèle haute-fidélité d’origine avec moins de 3% d’erreur, ce qui a permis de quantifier les incertitudes engendrées par la thermique.</p>
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