Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach
The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrif...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
|
| Series: | Data-Centric Engineering |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2632673623000175/type/journal_article |
| _version_ | 1797653315166666752 |
|---|---|
| author | Guy L. Bergel David Montes de Oca Zapiain Vicente Romero |
| author_facet | Guy L. Bergel David Montes de Oca Zapiain Vicente Romero |
| author_sort | Guy L. Bergel |
| collection | DOAJ |
| description | The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases. |
| first_indexed | 2024-03-11T16:42:50Z |
| format | Article |
| id | doaj.art-f3f38a3a5b414e5e8e7d68281ad9300b |
| institution | Directory Open Access Journal |
| issn | 2632-6736 |
| language | English |
| last_indexed | 2024-03-11T16:42:50Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Data-Centric Engineering |
| spelling | doaj.art-f3f38a3a5b414e5e8e7d68281ad9300b2023-10-23T08:50:05ZengCambridge University PressData-Centric Engineering2632-67362023-01-01410.1017/dce.2023.17Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approachGuy L. Bergel0https://orcid.org/0009-0006-7223-7631David Montes de Oca Zapiain1https://orcid.org/0000-0001-7890-0859Vicente Romero2Sandia National Laboratories, Livermore, CA, USASandia National Laboratories, Albuquerque, NM, USASandia National Laboratories, Albuquerque, NM, USAThe finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.https://www.cambridge.org/core/product/identifier/S2632673623000175/type/journal_articleBayesian neural networksfinite element methodneural network ensemblessurrogate modelsuncertainty quantificationvariational Bayesian inference |
| spellingShingle | Guy L. Bergel David Montes de Oca Zapiain Vicente Romero Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach Data-Centric Engineering Bayesian neural networks finite element method neural network ensembles surrogate models uncertainty quantification variational Bayesian inference |
| title | Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach |
| title_full | Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach |
| title_fullStr | Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach |
| title_full_unstemmed | Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach |
| title_short | Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach |
| title_sort | neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method neural network approach |
| topic | Bayesian neural networks finite element method neural network ensembles surrogate models uncertainty quantification variational Bayesian inference |
| url | https://www.cambridge.org/core/product/identifier/S2632673623000175/type/journal_article |
| work_keys_str_mv | AT guylbergel neuralnetworkensemblesanduncertaintyestimationforpredictionsofinelasticmechanicaldeformationusingafiniteelementmethodneuralnetworkapproach AT davidmontesdeocazapiain neuralnetworkensemblesanduncertaintyestimationforpredictionsofinelasticmechanicaldeformationusingafiniteelementmethodneuralnetworkapproach AT vicenteromero neuralnetworkensemblesanduncertaintyestimationforpredictionsofinelasticmechanicaldeformationusingafiniteelementmethodneuralnetworkapproach |