Abstract
An adaptive function estimation approach is presented to recover an unknown, multivariate functional relation from noisy data. Using a sparse grid combination approach, both discretization and Tikhonov regularization need to be selected appropriately to resolve functional details whilst suppressing measurement noise. An initially coarse, multivariate grid is adaptively refined using sensitivity analysis, creating a sequence of hierarchically refined grids. The problem of choosing a multi-dimensional discretization level is thus transformed to the identification of a suitable refinement step, giving rise to a nested approach for the selection of both discretization and Tikhonov regularization. Validation on multivariate test functions shows good approximation results.
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