Physics-informed two-tier neural network for non-linear model order reduction
Abstract In recent years, machine learning (ML) has had a great impact in the area of non-intrusive, non-linear model order reduction (MOR). However, the offline training phase often still entails high computational costs since it requires numerous, expensive, full-order solutions as the training da...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-11-01
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| Series: | Advanced Modeling and Simulation in Engineering Sciences |
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| Online Access: | https://doi.org/10.1186/s40323-024-00273-3 |
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| author | Yankun Hong Harshit Bansal Karen Veroy |
| author_facet | Yankun Hong Harshit Bansal Karen Veroy |
| author_sort | Yankun Hong |
| collection | DOAJ |
| description | Abstract In recent years, machine learning (ML) has had a great impact in the area of non-intrusive, non-linear model order reduction (MOR). However, the offline training phase often still entails high computational costs since it requires numerous, expensive, full-order solutions as the training data. Furthermore, in state-of-the-art methods, neural networks trained by a small amount of training data cannot be expected to generalize sufficiently well, and the training phase often ignores the underlying physical information when it is applied with MOR. Moreover, state-of-the-art MOR techniques that ensure an efficient online stage, such as hyper reduction techniques, are either intrusive or entail high offline computational costs. To resolve these challenges, inspired by recent developments in physics-informed and physics-reinforced neural networks, we propose a non-intrusive, physics-informed, two-tier deep network (TTDN) method. The proposed network, in which the first tier achieves the regression of the unknown quantity of interest and the second tier rebuilds the physical constitutive law between the unknown quantities of interest and derived quantities, is trained using pretraining and semi-supervised learning strategies. To illustrate the efficiency of the proposed approach, we perform numerical experiments on challenging non-linear and non-affine problems, including multi-scale mechanics problems. |
| format | Article |
| id | doaj-art-c1fa0e3cca7b41b18d1c89541b51f514 |
| institution | Kabale University |
| issn | 2213-7467 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advanced Modeling and Simulation in Engineering Sciences |
| spelling | doaj-art-c1fa0e3cca7b41b18d1c89541b51f5142024-11-17T12:38:41ZengSpringerOpenAdvanced Modeling and Simulation in Engineering Sciences2213-74672024-11-0111114910.1186/s40323-024-00273-3Physics-informed two-tier neural network for non-linear model order reductionYankun Hong0Harshit Bansal1Karen Veroy2Centre for Analysis, Scientific Computing and Applications, Eindhoven University of TechnologyCentre for Analysis, Scientific Computing and Applications, Eindhoven University of TechnologyCentre for Analysis, Scientific Computing and Applications, Eindhoven University of TechnologyAbstract In recent years, machine learning (ML) has had a great impact in the area of non-intrusive, non-linear model order reduction (MOR). However, the offline training phase often still entails high computational costs since it requires numerous, expensive, full-order solutions as the training data. Furthermore, in state-of-the-art methods, neural networks trained by a small amount of training data cannot be expected to generalize sufficiently well, and the training phase often ignores the underlying physical information when it is applied with MOR. Moreover, state-of-the-art MOR techniques that ensure an efficient online stage, such as hyper reduction techniques, are either intrusive or entail high offline computational costs. To resolve these challenges, inspired by recent developments in physics-informed and physics-reinforced neural networks, we propose a non-intrusive, physics-informed, two-tier deep network (TTDN) method. The proposed network, in which the first tier achieves the regression of the unknown quantity of interest and the second tier rebuilds the physical constitutive law between the unknown quantities of interest and derived quantities, is trained using pretraining and semi-supervised learning strategies. To illustrate the efficiency of the proposed approach, we perform numerical experiments on challenging non-linear and non-affine problems, including multi-scale mechanics problems.https://doi.org/10.1186/s40323-024-00273-3Physics-informed machine learningNeural networksNon-linear model order reductionHyper-reduction |
| spellingShingle | Yankun Hong Harshit Bansal Karen Veroy Physics-informed two-tier neural network for non-linear model order reduction Advanced Modeling and Simulation in Engineering Sciences Physics-informed machine learning Neural networks Non-linear model order reduction Hyper-reduction |
| title | Physics-informed two-tier neural network for non-linear model order reduction |
| title_full | Physics-informed two-tier neural network for non-linear model order reduction |
| title_fullStr | Physics-informed two-tier neural network for non-linear model order reduction |
| title_full_unstemmed | Physics-informed two-tier neural network for non-linear model order reduction |
| title_short | Physics-informed two-tier neural network for non-linear model order reduction |
| title_sort | physics informed two tier neural network for non linear model order reduction |
| topic | Physics-informed machine learning Neural networks Non-linear model order reduction Hyper-reduction |
| url | https://doi.org/10.1186/s40323-024-00273-3 |
| work_keys_str_mv | AT yankunhong physicsinformedtwotierneuralnetworkfornonlinearmodelorderreduction AT harshitbansal physicsinformedtwotierneuralnetworkfornonlinearmodelorderreduction AT karenveroy physicsinformedtwotierneuralnetworkfornonlinearmodelorderreduction |