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

• DOI: 10.1016/j.cma.2023.116657
• Publication Date: 2023-12-06T11:51:52Z
• Authors: Harshit Kapadia; Lihong Feng; Peter Benner
• Keywords: Surrogate model; Uncertainty Quantification; Model order reduction

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