Statistical closure modeling for reduced-order models of stationary\n systems by the ROMES method

2019/01/09 by Stefano Pagani, Andrea Manzoni, Pagani, Stefano +3 · 1 citation
Engineering · Physics and Astronomy · #Fault Detection and Control Systems #Model Reduction and Neural Networks #Advanced Control Systems Optimization

paper · pdf · doi:10.48550/arxiv.1901.02792

Abstract

This work proposes a technique for constructing a statistical closure model\nfor reduced-order models (ROMs) applied to stationary systems modeled as\nparameterized systems of algebraic equations. The proposed technique extends\nthe reduced-order-model error surrogates (ROMES) method to closure modeling.\nThe original ROMES method applied Gaussian-process regression to construct a\nstatistical model that maps cheaply computable error indicators (e.g., residual\nnorm, dual-weighted residuals) to a random variable for either (1) the norm of\nthe state error or (2) the error in a scalar-valued quantity of interest.\nRather than target these two types of errors, this work proposes to construct a\nstatistical model for the state error itself; it achieves this by constructing\nstatistical models for the generalized coordinates characterizing both the\nin-plane error (i.e., the error in the trial subspace) and a low-dimensional\napproximation of the out-of-plane error. The former can be considered a\nstatistical closure model, as it quantifies the error in the ROM generalized\ncoordinates. Because any quantity of interest can be computed as a functional\nof the state, the proposed approach enables any quantity-of-interest error to\nbe statistically quantified a posteriori, as the state-error model can be\npropagated through the associated quantity-of-interest functional. Numerical\nexperiments performed on both linear and nonlinear stationary systems\nillustrate the ability of the technique (1) to improve (expected) ROM\nprediction accuracy by an order of magnitude, (2) to statistically quantify the\nerror in arbitrary quantities of interest, and (3) to realize a more\ncost-effective methodology for reducing the error than a ROM-only approach in\nthe case of nonlinear systems.\n

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