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Uncertainty quantification

Physical systems typically have uncertainties in them, either in the specification of the model equations or input data to the equations. To properly capture the possible outcomes of the model, one needs to employ uncertainty quantifications. However, traditional uncertainty quantifications can require excessive runtime and it can be difficult to properly analyze the results.

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By now, there is a vast array of uncertainty quantification methods, but they often rely on regularity assumptions on the physical model that can be difficult to verify in practice. We offer expertise in selecting the best uncertainty quantification algorithm for the selected problem, with a special emphasis on Monte Carlo, quasi Monte Carlo and multilevel Monte Carlo. Furthermore, we can post-process (or in-situ process, where relevant) the data generated to compute derived quantities such as the probability density function. 

As complementary expertise, we can also incorporate observations through data assimilation, and hardware-accelerated numerics for dealing with low regularity problems. 

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