Efficient methods for optimal space filling in model reduction techniques

Abstract

Model reduction techniques generate low-dimensional models to parametrize PDEs in order to allow for efficient evaluation of highly non-linear problems in many-query and real-time context. Computing time in these methods is divided into a time consuming "off-line" phase needed to "train" a surrogate model, which is further used in "on-line" phase providing accurate results in a much faster way. The accuracy of these methods is strictly connected to the number of points in which the system response is previously computed and on their distribution in a parameter space. For a given number of analysis decided to be "invested" for the design of surrogate model, the accuracy can be further improved by the adequate distribution of them in a parameter space. Two methods of robust samples distribution are proposed here. A first method is based on interactive nodes aimed to optimize the distribution of them. A second is based on an optimal Latin hypercube design. Both presented methods are flexible with respect to the number of nodes involved and they can provide uniform distribution for any arbitrary number of them. Furthermore, they allow also for taking into account different importance of divers parameters.