Mathikolonis, Theodoros; (2020) Gaussian Process-based Optimization using Mutual Information for Computer Experiments. Application to Storm Surge extremes. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The computational burden of running a complex computer model can make optimization impractical. Gaussian Processes (GPs) are statistical surrogates (also known as emulators) that alleviate this issue since they cheaply replace the computer model. As a result, the exploration vs. exploitation trade-off strategy can be accelerated by building a GP surrogate. In the current study, we propose a new surrogate-based optimization scheme that minimizes the number of evaluations of the computationally expensive function. Taking advantage of parallelism of the evaluation of the unknown function, the uncertain regions are explored simultaneously, and a batch of input points is chosen using Mutual Information for Computer Experiments (MICE), a sequential design algorithm which maximizes the in- formation theoretic Mutual Information over the input space. The computational efficiency of interweaving the optimization scheme with MICE (optim-MICE) is examined and demonstrated on test functions. Optim-MICE is compared with state- of-the-art heuristics. We demonstrate that optim-MICE outperforms the alternative schemes on a large range of computational experiments. The proposed algorithm is also employed to study the extrema of coastal storm waves, such as the ones that ob- served during Typhoon Haiyan (2013, Philippines). A stretch of coral reef near the coast, which was expected to protect the coastal communities, actually amplified the waves. The propagation and breaking process of such large nearshore waves can be successfully captured by a phase-resolving wave model. However, the computational complexity of the simulator makes optimization tasks impractical. The optim-MICE algorithm is therefore used to find the maximum breaking wave (bore) height and the maximum run-up. In two idealised settings, we efficiently identify the conditions that create the largest storm waves at the coast using a minimal number of simulations. This is the first surrogate-based optimization of storm waves and it opens the door to previously inconceivable coastal risk assessments.

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