Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

05/12/2020
by   Wayne Isaac Tan Uy, et al.
0

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. 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/28/2022

An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations

In this paper, a nonsmooth semilinear parabolic partial differential equ...
research
10/31/2021

Reduced Order Model Predictive Control for Parametrized Parabolic Partial Differential Equations

Model Predictive Control (MPC) is a well-established approach to solve i...
research
08/29/2019

Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference

This work introduces a method for learning low-dimensional models from d...
research
02/27/2020

Model order reduction for parametric high dimensional models in the analysis of financial risk

This paper presents a model order reduction (MOR) approach for high dime...
research
03/15/2020

Low-dimensional approximations of high-dimensional asset price models

We consider high-dimensional asset price models that are reduced in thei...
research
02/09/2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on com...
research
03/01/2022

E-LMC: Extended Linear Model of Coregionalization for Predictions of Spatial Fields

Physical simulations based on partial differential equations typically g...

Please sign up or login with your details

Forgot password? Click here to reset