Uncertainty Quantification in Computational Predictive Science
Americo Cunha Jr Assistant Professor of Applied Mathematics
Institute of Mathematics and Statistics
Rio de Janeiro State University (UERJ)
Nowadays computational predictive models are standard tools for analysis of complex systems and phenomena, which have been extensively used by industry and academy. However, any computational model is uncertain with respect to the system/phenomenon of interest, due to variabilities on its parameters and, mainly, because of the assumption made on its conception that may not be in agreement with reality. The first source of uncertainty is inherent to measurements limitations, imperfections in manufacturing process, material and geometric variabilities, etc. Meanwhile, the second type is essentially due to lack of knowledge about the underlying governing laws. Provide a precise characterization of these uncertainties and quantify their impact on the computational predictions made about the system of interest is often a challenging task. Uncertainty Quantification (UQ) can be thought of as a multi-disciplinary area that deals with quantitative characterization and reduction of uncertainties in applications, which is extremely necessary to give robustness to computational forecasts. The lectures will cover the basic vocabulary of UQ, the possible approaches to modeling uncertainties, the main techniques for uncertainty propagation. Basic topics of probability and statistics will be reviewed.Computer activities will be developed in parallel to theoretical expositions, as a way to give a hands-on tone to the course.
Dr. Americo Cunha is an Assistant Professor of Applied Mathematics at Rio de Janeiro State University (UERJ) in Brazil, co-founder and coordinator of the Nucleus of Modeling and Experimentation with Computers – NUMERICO. His research interests include computational science and engineering, uncertainty quantification, nonlinear dynamics, inverse problems and industrial mathematics. Dr. Cunha has B. Eng., M.Sc. and D.Sc. degrees in Mechanical Engineering from Pontifical Catholic University of Rio de Janeiro (PUC-Rio) in Brazil, where he also obtained a B.Sc. degree in Applied Mathematics. He keeps academic collaboration with research groups in Brazil, France and USA.