A non-intrusive bi-fidelity reduced basis method for time-independent problems

by   Jun Sur Richard Park, et al.

Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively expensive, especially for large-scale complex applications. To address this issue, reduced order modeling (ROM) has emerged as an effective method to reduce computational costs. However, ROM often requires significant modifications to the existing code, which can be time-consuming and complex, particularly for large-scale legacy codes. Non-intrusive methods have gained attention as an alternative approach. However, most existing non-intrusive approaches are purely data-driven and may not respect the underlying physics laws during the online stage, resulting in less accurate approximations of the reduced solution. In this study, we propose a new non-intrusive bi-fidelity reduced basis method for time-independent parametric PDEs. Our algorithm utilizes the discrete operator, solutions, and right-hand sides obtained from the high-fidelity legacy solver. By leveraging a low-fidelity model, we efficiently construct the reduced operator and right-hand side for new parameter values during the online stage. Unlike other non-intrusive ROM methods, we enforce the reduced equation during the online stage. In addition, the non-intrusive nature of our algorithm makes it straightforward and applicable to general nonlinear time-independent problems. We demonstrate its performance through several benchmark examples, including nonlinear and multiscale PDEs.


page 19

page 23


Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference

This work formulates a new approach to reduced modeling of parameterized...

Deep Convolutional Architectures for Extrapolative Forecast in Time-dependent Flow Problems

Physical systems whose dynamics are governed by partial differential equ...

Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks

We propose a nonlinear reduced basis method for the efficient approximat...

Error estimate of the Non Intrusive Reduced Basis method with finite volume schemes

The context of this paper is the simulation of parameter-dependent parti...

Error estimate of the Non-Intrusive Reduced Basis (NIRB) two-grid method with parabolic equations

Reduced Basis Methods (RBMs) are frequently proposed to approximate para...

The non-intrusive reduced basis two-grid method applied to sensitivity analysis

This paper deals with the derivation of Non-Intrusive Reduced Basis (NIR...

Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and ...

Please sign up or login with your details

Forgot password? Click here to reset