Automatic Surrogate Model Building for Computer based Design

For many problems from science and engineering it is impractical to perform experiments on the physical world directly (e.g., airfoil design, earthquake propagation). Instead, complex, physics-based simulation codes are used to run experiments on computer hardware. While allowing scientists more flexibility to study phenomena under controlled conditions, computer experiments require a substantial investment of computation time (one simulation may take many minutes, hours, days or even weeks). This is especially evident for routine tasks such as optimization, sensitivity analysis and design space exploration [1]. As a result, the use of various approximation methods that mimic the behavior of the simulation model as closely as possible (while being computationally cheaper to evaluate), has become standard practice. This work concentrates on the use of data-driven, global1 approximations using compact surrogate models (also known as metamodels, or response surface models (RSM)). Examples include: rational functions, Kriging models, and Support Vector Machines (SVM). Once they are constructed, global surrogate models provide a fast and efficient way for the engineer to explore the relationship between parameters (design space exploration), study the influence of various boundary conditions on different optimization runs, or enable the simulation of large scale systems where this would normally be too cumbersome. For the last case a classic example is the full-wave simulation of an electronic circuit board. Electro-magnetic modeling of the whole board in one run is almost intractable. Instead the board is modeled as a collection of small, compact, accurate replacement surrogate models that represent the different functional components (capacitors, resistors, ...) on the board. In this way simulations can be literally pieced together. However, in order to come to an acceptable approximation, numerous problems and design choices need to be overcome: what data collection strategy to use, what model type is most applicable, how should model parameters be tuned, how to optimize the accuracy vs computational cost trade-off, etc. Particularly important is the data collection strategy. Since data is computationally expensive to obtain, data points must be selected iteratively, there where the information gain will be the greatest. A Note the difference between global surrogate modeling as opposed to local surrogate modeling. In the global case, optimization is not the goal but rather a consequence. The accuracy requirements are also higher and the data collection strategy is different. Nevertheless the two are not disjunct, advances in one type can provide insights for the other.