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Engineering Design via Surrogate Modelling: A Practical Guide

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Think of a well-known public personality whom you could easily identify from a photograph. Consider now whether you would still recognize them if most of the photograph was obscured, except for the corner of an eye, a small part of their chin and, perhaps, a half of their mouth. This is a game often played on television quiz shows and some contestants (and viewers at home) often display an uncanny ability to come up with the correct name after only a few small sections of the picture are revealed.

This is a demonstration of the brain’s astounding ability to fill in blanks by subconsciously constructing a surrogate model of the full photograph, based on a few samples of it. The key to such apparently impressive feats is that we actually know a great deal about the obscured parts. We know that the photograph represents a human face, that is the image is likely to be roughly symmetrical, and we know that somewhere in the middle there must be a pattern we usually refer to as a ‘nose’, etc. Moreover, we know that it is a famous face. The ‘search space’ thus reduced, the task seems a lot easier.

The surrogate models that form the subject of this book are educated guesses as to what an engineering function might look like, based on a few points in space where we can afford to measure the function values. While these glimpses alone would not tell us much, they become very useful if we build a number of assumptions into the surrogate based on our experience of what such functions tend to look like. For example, they tend to be continuous. We may also assume that their derivatives are continuous too. With such assumptions built into the learner, the surrogate model becomes a very effective low cost replacement of the original function for a wide variety of purposes.

Surrogate modelling has had a great impact on the way the authors think about design and, after many years of combined experience in the subject, it has become a fundamental element of our engineering thought processes. We wrote this book as a means of sharing some of this experience on a practical level. While a lot has been written about the deeper theoretical aspects of surrogate modelling (indeed, references are included throughout this text to the landmarks of this literature that have informed our own thinking), what we strove to offer here is a manual for the practitioner wishing to get started quickly on solving their own engineering problems. Of course, like any sharp tool, surrogate modelling can only be used in a scientifically rigorous way if the user is constantly aware of its dangers, pitfalls, potential false promises and limitations – the present text goes to great lengths to point these out at the appropriate times.
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