Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
Abstract
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. Here, the computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions.
- Publication Date:
- Research Org.:
- New York Univ., NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1784724
- Grant/Contract Number:
- SC0019334
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Mathematical Modelling and Numerical Analysis
- Additional Journal Information:
- Journal Volume: 55; Journal Issue: 3; Journal ID: ISSN 0764-583X
- Publisher:
- EDP Sciences
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Uy, Wayne Isaac Tan, and Peherstorfer, Benjamin. Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations. United States: N. p., 2021.
Web. doi:10.1051/m2an/2021010.
Uy, Wayne Isaac Tan, & Peherstorfer, Benjamin. Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations. United States. https://doi.org/10.1051/m2an/2021010
Uy, Wayne Isaac Tan, and Peherstorfer, Benjamin. Wed .
"Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations". United States. https://doi.org/10.1051/m2an/2021010. https://www.osti.gov/servlets/purl/1784724.
@article{osti_1784724,
title = {Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations},
author = {Uy, Wayne Isaac Tan and Peherstorfer, Benjamin},
abstractNote = {This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. Here, the computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions.},
doi = {10.1051/m2an/2021010},
journal = {Mathematical Modelling and Numerical Analysis},
number = 3,
volume = 55,
place = {United States},
year = {Wed May 05 00:00:00 EDT 2021},
month = {Wed May 05 00:00:00 EDT 2021}
}
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