An Adaptive Sampling Approach for the Reduced Basis Method

Chellappa, Sridhar; Feng, Lihong; Benner, Peter

doi:10.1007/978-3-030-95157-3_8

Cited by 13 publications

(40 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, many efforts have been made in this direction to develop computable error estimators for different problems [15,16,18,19,20,21,22,23,24,25,28,33,34,35]. However, more attention has been paid to improve the effectivity or accuracy of the error estimator than to develop more efficient strategies to accelerate the greedy process [13,25,33,34,36]. Recently, some techniques are proposed to improve the adaptivity of the greedy algorithm [6,7,13,26].…”

Section: Introductionmentioning

confidence: 99%

“…However, more attention has been paid to improve the effectivity or accuracy of the error estimator than to develop more efficient strategies to accelerate the greedy process [13,25,33,34,36]. Recently, some techniques are proposed to improve the adaptivity of the greedy algorithm [6,7,13,26].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In [13,14], we proposed a surrogate model for error estimation, and proposed an adaptive greedy algorithm by alternatively using this surrogate error estimator and the original error estimator during the greedy algorithm. The focus in [13,14] was to make the greedy process adaptive by starting from a coarse training set of a small number of parameter samples, and adaptively update the coarse training set with the aid of a surrogate error estimator. The original error estimator is computed only over the coarse training set, while the surrogate error estimator helps to pick out candidates of important parameter samples from a fine training set, which are then collected in the coarse training set.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we emphasize the role of the surrogate error estimator and propose the concept of bi-fidelity error estimation and multi-fidelity error estimation. In fact, a bi-fidelity error estimation has been used in the adaptive greedy algorithm proposed in [13,14] without being formally defined, i.e., the original (high-fidelity) error estimator, and the surrogate (low-fidelity) error estimator. To further improve the convergence speed of the greedy algorithm, we propose multi-fidelity error estimation built upon the bi-fidelity error estimation.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multi-fidelity error estimation accelerates greedy model reduction of complex dynamical systems

Li¹,

Lombardi²,

Antonini³

et al. 2023

Preprint

View full text Add to dashboard Cite

Model order reduction usually consists of two stages: the offline stage and the online stage. The offline stage is the expensive part that sometimes takes hours till the final reduced-order model is derived, especially when the original model is very large or complex. Once the reduced-order model is obtained, the online stage of querying the reduced-order model for simulation is very fast and often real-time capable. This work concerns a strategy to significantly speed up the offline stage of model order reduction for large and complex systems. In particular, it is successful in accelerating the greedy algorithm that is often used in the offline stage for reduced-order model construction. We propose multi-fidelity error estimators and replace the high-fidelity error estimator in the greedy algorithm. Consequently, the computational complexity at each iteration of the greedy algorithm is reduced and the algorithm converges more than 3 times faster without incurring noticeable accuracy loss.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multi-fidelity error estimation accelerates greedy model reduction of complex dynamical systems

Li¹,

Lombardi²,

Antonini³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Fast and reliable reduced‐order models for cardiac electrophysiology

Chellappa,

Cansız,

Feng

et al. 2023

GAMM-Mitteilungen

Self Cite

View full text Add to dashboard Cite

Mathematical models of the human heart increasingly play a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The ultimate aim is to aid medical practitioners diagnose and treat the many ailments affecting the heart. Towards this, modeling cardiac electrophysiology is crucial as the heart's electrical activity underlies the contraction mechanism and the resulting pumping action. Apart from modeling attempts, the pursuit of efficient, reliable, and fast solution algorithms has been of great importance in this context. The governing equations and the constitutive laws describing the electrical activity in the heart are coupled, nonlinear, and involve a fast moving wave front, which is generally solved by the finite element method. The numerical treatment of this complex system as part of a virtual heart model is challenging due to the necessity of fine spatial and temporal resolution of the domain. Therefore, efficient surrogate models are needed to predict the electrical activity in the heart under varying parameters and inputs much faster than the finely resolved models. In this work, we develop an adaptive, projection‐based reduced‐order surrogate model for cardiac electrophysiology. We introduce an a posteriori error estimator that can accurately and efficiently quantify the accuracy of the surrogate model. Using the error estimator, we systematically update our surrogate model through a greedy search of the parameter space. Furthermore, using the error estimator, the parameter search space is dynamically updated such that the most relevant samples get chosen at every iteration. The proposed adaptive surrogate model is tested on three benchmark models to illustrate its efficiency, accuracy, and ability of generalization.

show abstract

Multi‐fidelity error estimation accelerates greedy model reduction of complex dynamical systems

Feng,

Lombardi,

Antonini

et al. 2023

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Model order reduction usually consists of two stages: the offline stage and the online stage. The offline stage is the expensive part that sometimes takes hours till the final reduced‐order model is derived, especially when the original model is very large or complex. Once the reduced‐order model is obtained, the online stage of querying the reduced‐order model for simulation is very fast and often real‐time capable. This work concerns a strategy to speed up the offline stage of model order reduction for large and complex systems. In particular, it is successful in accelerating the greedy algorithm that is often used in the offline stage for reduced‐order model construction. We propose to replace the high‐fidelity error estimator in the greedy algorithm with multi‐fidelity error estimation. Consequently, the computational complexity of the greedy algorithm is reduced and the algorithm converges more than two times faster without incurring noticeable accuracy loss.

show abstract

An Adaptive Sampling Approach for the Reduced Basis Method

Cited by 13 publications

References 20 publications

Multi-fidelity error estimation accelerates greedy model reduction of complex dynamical systems

Multi-fidelity error estimation accelerates greedy model reduction of complex dynamical systems

Fast and reliable reduced‐order models for cardiac electrophysiology

Multi‐fidelity error estimation accelerates greedy model reduction of complex dynamical systems

Contact Info

Product

Resources

About