# A non-intrusive reduced-order modeling method using polynomial chaos expansion

## TL;DR

This paper introduces a non-intrusive reduced-order modeling approach combining POD and PCE to efficiently perform uncertainty quantification with reduced computational costs and high accuracy.

## Contribution

It presents a novel non-intrusive method integrating POD and PCE for stochastic modeling, reducing costs while maintaining accuracy in UQ analysis.

## Key findings

- Significantly reduces computational costs and storage requirements.
- Achieves similar accuracy to full-PCE in statistical predictions.
- Effectively predicts outputs using only a few snapshots.

## Abstract

We propose a non-intrusive reduced-order modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides an optimally ordered basis from a set of selected full-order snapshots. Truncating this optimal basis, we construct a reduced-order model with undetermined coefficients. Then, PCE is utilized to approximate the coefficients of the truncated basis. In the proposed method, we construct a PCE using a non-intrusive regression-based method. Combined with the model reduction ability of POD, the proposed method efficiently provides stochastic representations in UQ analysis. To investigate the performance of the proposed method, we provide three numerical examples, i.e., a highly nonlinear analytical function with three uncertain parameters, two-dimensional (2D) heat-driven cavity flow with a stochastic boundary temperature, and 2D heat diffusion with stochastic conductivity. The results demonstrate that the proposed method significantly reduces the computational costs and storage requirements that arise due to high-dimensional physical and random spaces. While demonstrating a similar accuracy with that of the classical full-PCE in predicting statistical quantities. Furthermore, the proposed method reasonably predict the outputs of the full order model using only a few snapshots.