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A methodology for using random sketching in the context of model orderreduction for high-dimensional parameter-dependent systems of equations wasintroduced in [Balabanov and Nouy 2019, Part I]. Following this framework, wehere construct a reduced model from a small, efficiently computable randomobject called a sketch of a reduced model, using minimal residual methods. Weintroduce a sketched version of the minimal residual based projection as wellas a novel nonlinear approximation method, where for each parameter value, thesolution is approximated by minimal residual projection onto a subspace spannedby several vectors picked (online) from a dictionary of candidate basisvectors. It is shown that random sketching technique can improve not onlyefficiency but also numerical stability. A rigorous analysis of the conditionson the random sketch required to obtain a given accuracy is presented. Theseconditions may be ensured a priori with high probability by considering for thesketching matrix an oblivious embedding of sufficiently large size.Furthermore, a simple and reliable procedure for a posteriori verification ofthe quality of the sketch is provided. This approach can be used forcertification of the approximation as well as for adaptive selection of thesize of the random sketching matrix.

Randomized linear algebra for model reduction. Part II: minimal residual methods and dictionary-based approximation