Computational strategies for constructing emulators of complex high-dimensional engineering systems

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When engineers build computer models of real-world engineering systems, they wish to do more than just predict the nominal performance of a single design: they also wish to predict what happens when the design parameters are changed, study the impact of uncertainty on system performance and safety, and ultimately carry out design improvement studies to optimize performance. However, a major obstacle to the successful adoption of computational modeling tools in engineering design practice is computational cost. It is not always practically feasible to run a high-fidelity computational model thousands of times to study various design alternatives or to examine performance variability. This obstacle is becoming more challenging since the fidelity with which engineers desire to model engineering systems has kept pace with advances in computer hardware. A very promising approach for tackling the computational cost issue is through the use of an emulator. An emulator is an approximation model of the original computational model that can be evaluated very cheaply (ideally in real-time). In practically important applications such as uncertainty analysis, design optimization and inverse parameter estimation, where the computer model needs to be run at several points in the parameter space, emulators can thus mitigate the problem of computational expense. The proposed research program will address the key fundamental, theoretical issues and computational challenges in this area in order to develop novel computational strategies for constructing emulators of a broad class of complex, high-dimensional engineering systems. The key elements of the proposed research program will include: (i) Bayesian methods for constructing emulators of the spatio-temporal response of black-box systems; (ii) Galerkin projection schemes for nonlinear, time-dependent parameterized systems; (iii) numerical methods for operator equations defined over parameterized domains; (iv) adaptive function decomposition strategies for circumventing the curse of dimensionality; and (v) parallel implementation of the algorithms developed and application to a range of real-world engineering problems.