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Applied Math Graduate Student Seminar: Walker Powell, NC State, Model Reduction and Validation Tools for Large-Scale Models
April 10 | 3:00 pm - 4:00 pm EDT
Of primary importance in computational science and applications is quantification and improvement of predictive capabilities of large-scale parameterized models, which often require the use of multi-query techniques that are intractable for computationally expensive models. This research focuses on three primary thrusts: sensitivity analysis, reduced-order modeling, and uncertainty quantification and algorithm and implementation choices that scale favorably relative to the computational complexity of the large-scale models. Together, these techniques can be used to robustly validate models and quantify uncertainty in their predictions in future data regimes. To this end, we propose quasi-global sensitivity analysis of large-scale dynamical systems, which aims to find parameters that significantly impact the dynamical behavior of solution trajectories. Additionally, we propose the construction of parametric POD-ROMs for use in delay-diffusion PDEs as potential surrogate models for use in multi-query applications. Finally, we propose the use of measure transport and Bayesian inference for efficient generation of “virtual populations,” that is, samples of model parameters who map to observed data distribution under the application of the model.