Active-learning-driven surrogate modeling for efficient simulation of parametric nonlinear systems

Abstract

When repeated evaluations for varying parameter configurations of a high-fidelity physical model are required, surrogate modeling techniques based on model order reduction are desirable. In absence of the governing equations describing the dynamics, we need to construct the parametric reduced-order surrogate model in a non-intrusive fashion. In this setting, the usual residual-based error estimate for optimal parameter sampling associated with the reduced basis method is not directly available. Our work provides a non-intrusive error-estimator-based optimality criterion to efficiently populate the parameter snapshots, thereby, enabling us to effectively construct a parametric surrogate model. We consider parameter-specific proper orthogonal decomposition subspaces and propose an active-learning-driven surrogate model using kernel-based shallow neural networks (KSNNs), abbreviated as ActLearn-POD-KSNN surrogate model. The center location for each kernel, along with center-dependent kernel widths, can be learned for the KSNN by using an alternating dual-staged iterative training procedure. To demonstrate the efficiency of our proposed ideas, we present numerical experiments using four physical models, including incompressible Navier–Stokes equations. The ActLearn-POD-KSNN surrogate model efficiently predicts the solution at new parameter locations, even for a setting with multiple interacting shock profiles and a fluid flow scenario with Hopf bifurcation. We also provide an investigation of the surrogate’s performance when the available data is noisy.