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Data-Driven Model Reduction, Scientific Frontiers, and Applications

Horacio Florez, Harold Vance Department of Petroleum Engineering
Uncertainty Quantification and Model-Order Reduction on Linear and Nonlinear Problems: Analysis, Approaches, and Challenges


Underbody blast simulations are complex and involve solving large nonlinear algebraic systems. Model order-reduction (MOR) is a projection based approach. We first execute an expensive, "offline" stage, where we study the full-order model (FOM). We then perform the cheap "online" stage upon creating a reduced-order basis (ROB). In this talk, we rediscover a regularization procedure and a globalization strategy to improve the Newton method convergence. We compute a reduced-order model (ROM) using discrete wavelets and the method of the snapshots via POD. Applications encompass the Bratu nonlinear models, single-phase flow, and nonlinear heat transfer with extensions to combustion problems. We aim to exploit the idle CPU time that MOR creates to perform uncertainty quantification based on stochastic approaches. The presentation summarizes two years of post-doctoral research work at the Army Research Laboratory and UTEP.