On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order Modeling
A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built incrementally starting from a moderate set of evaluations of the full...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2019-05-01
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| Series: | Frontiers in Materials |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fmats.2019.00075/full |
| _version_ | 1818329148169388032 |
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| author | Felix Fritzen Mauricio Fernández Fredrik Larsson |
| author_facet | Felix Fritzen Mauricio Fernández Fredrik Larsson |
| author_sort | Felix Fritzen |
| collection | DOAJ |
| description | A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built incrementally starting from a moderate set of evaluations of the full order model. Therefore, a reduced order model (ROM) is generated. Using a hybrid ROM-preconditioned FE solver additional effective stress-strain data is simulated while the number of samples is kept to a moderate level by using a dedicated and physics-guided sampling technique. Machine learning (ML) is subsequently used to build the second surrogate by means of artificial neural networks (ANN). Different ANN architectures are explored and the features used as inputs of the ANN are fine tuned in order to improve the overall quality of the ML model. Additional ML surrogates for the stress errors are generated. Therefore, conservative design guidelines for error surrogates are presented by adapting the loss functions of the ANN training in pure regression or pure classification settings. The error surrogates can be used as quality indicators in order to adaptively select the appropriate—i.e., efficient yet accurate—surrogate. Two strategies for the on-the-fly switching are investigated and a practicable and robust algorithm is proposed that eliminates relevant technical difficulties attributed to model switching. The provided algorithms and ANN design guidelines can easily be adopted for different problem settings and, thereby, they enable generalization of the used machine learning techniques for a wide range of applications. The resulting hybrid surrogate is employed in challenging multilevel FE simulations for a three-phase composite with pseudo-plastic micro-constituents. Numerical examples highlight the performance of the proposed approach. |
| first_indexed | 2024-12-13T12:43:27Z |
| format | Article |
| id | doaj.art-9ed463b81d2e42368473b5a3a4cc1026 |
| institution | Directory Open Access Journal |
| issn | 2296-8016 |
| language | English |
| last_indexed | 2024-12-13T12:43:27Z |
| publishDate | 2019-05-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Materials |
| spelling | doaj.art-9ed463b81d2e42368473b5a3a4cc10262022-12-21T23:45:34ZengFrontiers Media S.A.Frontiers in Materials2296-80162019-05-01610.3389/fmats.2019.00075452690On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order ModelingFelix Fritzen0Mauricio Fernández1Fredrik Larsson2EMMA - Efficient Methods for Mechanical Analysis, Institute of Applied Mechanics, University of Stuttgart, Stuttgart, GermanyEMMA - Efficient Methods for Mechanical Analysis, Institute of Applied Mechanics, University of Stuttgart, Stuttgart, GermanyMaterial and Computational Mechanics, Department of Industrial and Materials Science, Chalmers University of Technology, Göteborg, SwedenA multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built incrementally starting from a moderate set of evaluations of the full order model. Therefore, a reduced order model (ROM) is generated. Using a hybrid ROM-preconditioned FE solver additional effective stress-strain data is simulated while the number of samples is kept to a moderate level by using a dedicated and physics-guided sampling technique. Machine learning (ML) is subsequently used to build the second surrogate by means of artificial neural networks (ANN). Different ANN architectures are explored and the features used as inputs of the ANN are fine tuned in order to improve the overall quality of the ML model. Additional ML surrogates for the stress errors are generated. Therefore, conservative design guidelines for error surrogates are presented by adapting the loss functions of the ANN training in pure regression or pure classification settings. The error surrogates can be used as quality indicators in order to adaptively select the appropriate—i.e., efficient yet accurate—surrogate. Two strategies for the on-the-fly switching are investigated and a practicable and robust algorithm is proposed that eliminates relevant technical difficulties attributed to model switching. The provided algorithms and ANN design guidelines can easily be adopted for different problem settings and, thereby, they enable generalization of the used machine learning techniques for a wide range of applications. The resulting hybrid surrogate is employed in challenging multilevel FE simulations for a three-phase composite with pseudo-plastic micro-constituents. Numerical examples highlight the performance of the proposed approach.https://www.frontiersin.org/article/10.3389/fmats.2019.00075/fullreduced order modeling (ROM)machine learningartificial neural networks (ANN)surrogate modelingerror controlon-the-fly model adaptivity |
| spellingShingle | Felix Fritzen Mauricio Fernández Fredrik Larsson On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order Modeling Frontiers in Materials reduced order modeling (ROM) machine learning artificial neural networks (ANN) surrogate modeling error control on-the-fly model adaptivity |
| title | On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order Modeling |
| title_full | On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order Modeling |
| title_fullStr | On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order Modeling |
| title_full_unstemmed | On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order Modeling |
| title_short | On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order Modeling |
| title_sort | on the fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling |
| topic | reduced order modeling (ROM) machine learning artificial neural networks (ANN) surrogate modeling error control on-the-fly model adaptivity |
| url | https://www.frontiersin.org/article/10.3389/fmats.2019.00075/full |
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