Computational and machine learning methods for model reduction, uncertainty propagation, and parameter identification in fluid and solid mechanics

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Most fluid and solid problems in engineering modeling are described by time-dependent and parametrized nonlinear partial differential equations. Their resolution with traditional computational mechanics methods may be too expensive, especially in the context of predictions with uncertainty quantification or optimization, to allow for rapid predictions. We propose to investigate advanced machine learning methods aimed at representing high-fidelity computational models by means of reduced-dimension surrogate ones. In addition, different approaches will be studied for the uncertainty quantification. Indeed, reliable modeling predictions of natural and industrial processes should include quantification of the uncertainties that may arise from various sources. This program also supports a continuous interest in parallel computing to enable rapid predictions for large-scale simulations. While these proposed activities are geared towards developing new approaches and algorithms, the research program is also application-driven. We will focus on two challenging engineering applications, motivated by real needs. However, the proposed methods  will not be restricted to these applications. - Probabilistic flooding maps using machine learning: Floods are among the costliest natural disasters. Governments and agencies are therefore required to develop reliable and accurate maps of flood risk areas as part of their preventive measures. The main objective here is to develop predictive tools that combine advanced computational methods with machine learning to establish accurate maps with probabilistic information; and, in the case of an extreme emergency event, to allow rapid predictions, almost in real-time. - Physical parameter identification: The constitutive parameters used in the modeling of complex systems are often associated with high degrees of uncertainties. Inverse analysis provides a way to identify these parameters. We consider the identification and optimization of the numerous parameters involved in the selective laser melting (SLM) additive manufacturing process. Additive manufacturing is a modern technology that has been used across a diverse range of industries, including automotive, aerospace and medical, among others. It is anticipated that this research program will contribute to the advancement of knowledge about several aspects of numerical modeling, machine learning and parameter optimization, and add to the analysis of uncertainties in hydraulics and additive manufacturing. The training of highly qualified personnel (5 Ph.D.s, one postdoctoral fellow, 2 M.SC students and 5 undergraduate students) will be beneficial to society as a whole, as well as to relevent industries in Canada. There is a great potential for a number of innovative publications and collaborations with industrial partners. This research will also result in the development of high-performance codes that can be used for even more research and applied projects.