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Abstract:
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Computer models, or codes, are used to provide numerical solutions to mathematical models describing real-world problems. Some codes are computationally intensive, reflecting the complexities of mathematical models. Fast approximations, or surrogates, are often used to alleviate the computational burden. We propose multi-output physics-based Kriging surrogates for a class of finite element models, using code information about the underlying partial differential equation in a statistics framework. Specifically, the contribution of our paper consists in applying Kriging methods to deviation vectors of linearly-transformed fine-mesh solutions retained on a coarse mesh, where the transformation is defined in terms of coarse-mesh stiffness matrices and load vectors. The accuracy of the surrogate is supported by a convergence result. We use Darcy's equation to illustrate the method. Based on a moderate sample of 50 inputs, the proposed FEM-dev surrogate has a root mean square error lower by about 40% than its multi-output competitors direct regression surrogate and basis decomposition surrogate. In addition, it has prediction interval coverage closer to the nominal values than its competitors.
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