Uncertainty Quantification for Black Box Models

Uncertainty Quantification for Black Box Models




Using statistical uncertainty quantification methods for computationally-expensive engineering problems.


Some PDE-based models in engineering are extremely challenging and expensive to solve, and are often characterised by high-dimensional input and output spaces. We aim to tailor existing methods from the emulation and calibration literature to such problems, providing full-field predictions of the model output at a fraction of the cost of solving the model directly. 


With the ability to predict the full model output (with uncertainty) at a particular setting of the input parameters via an emulator, such an emulator can be used as a proxy for the true model in many applications that are currently hindered by a high computational cost. For example, in problems requiring domain decomposition, where the model is solved on a large number of subdomains, an emulator proxy can be used in place of the exact solution on every subdomain, with full solutions (unobtainable or extremely expensive directly) constructed from the individual emulators, incorporating the correlation structure between the different subdomains. How best to include this structure is an area of ongoing research within this project.



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