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When repeated evaluations for varying parameter configurations of ahigh-fidelity physical model are required, surrogate modeling techniques basedon model order reduction are desired. In absence of the governing equationsdescribing the dynamics, we need to construct the parametric reduced-ordersurrogate model in a non-intrusive fashion. In this setting, the usualresidual-based error estimate for optimal parameter sampling associated withthe reduced basis method is not directly available. Our work provides anon-intrusive optimality criterion to efficiently populate the parametersnapshots, thereby, enabling us to effectively construct a parametric surrogatemodel. We consider separate parameter-specific proper orthogonal decomposition(POD) subspaces and propose an active-learning-driven surrogate model usingkernel-based shallow neural networks, abbreviated as ActLearn-POD-KSNNsurrogate model. To demonstrate the validity of our proposed ideas, we presentnumerical experiments using two physical models, namely Burgers' equation andshallow water equations. Both the models have mixed -- convective and diffusive-- effects within their respective parameter domains, with each of themdominating in certain regions. The proposed ActLearn-POD-KSNN surrogate modelefficiently predicts the solution at new parameter locations, even for asetting with multiple interacting shock profiles.

Active-Learning-Driven Surrogate Modeling for Efficient Simulation of Parametric Nonlinear Systems