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In this paper, we propose a new approach to model reduction of parameterizedpartial differential equations (PDEs) based on the concept of adaptive reducedbases. The presented approach is particularly suited for large-scale nonlinearsystems characterized by parameter variations. Instead of using a global basisto construct a global reduced model, the proposed method approximates theoriginal system by multiple lower-dimensional subspaces. Each localized reducedbasis is generated by the SVD of a weighted snapshot ensemble; here, eachweighting coefficient is a function of the input parameter. Compared with aglobal model reduction method, such as the classical POD, the adaptive modelreduction method could yield a more accurate solution with a fixed subspacedimension. Moreover, we combine the adaptive reduced model with the chorditeration to solve elliptic PDEs in a computationally efficient fashion. Thepotential of the method for achieving large speedups, while maintaining goodaccuracy, is demonstrated for both elliptic and parabolic PDEs in a fewnumerical examples.

Nonlinear Model Reduction via an Adaptive Weighting of Snapshots