HORUS - high-dimensional Model Order Reduction via low moment-matching upgraded sampling

This paper describes a Model Order Reduction algorithm for multi-dimensional parameterized systems, based on a sampling procedure which incorporates a low order moment matching paradigm into a multi-point based methodology. The procedure seeks to maximize the subspace generated by a given number of samples, selected among an initial candidate set. The selection is based on a global criteria that chooses the sample whose associated vector adds more information to the existing subspace. However, the initial candidate set can be extremely large for high-dimensional systems, and thus the procedure can be costly. To improve efficiency we propose a scheme to incorporate information from low order moments to the basis with small extra cost, in order to extend the approximation to a wider region around the selected point. This will allow reduction of the initial candidate set without decreasing the level of confidence. We further improve the procedure by generating the global subspace based on the composition of local approximations. To achieve this, the initial candidates will be split into subsets that will be considered as independent regions, and in a first phase the procedure applied locally thus enabling improved efficiency and providing a framework for almost perfect parallelization.