Physics-informed deep learning for one-dimensional consolidation
Neural networks with physical governing equations as constraints have recently created a new trend in machine learning research. In this context, a review of related research is first presented and discussed. The potential offered by such physics-informed deep learning models for computations in geo...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-04-01
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| Series: | Journal of Rock Mechanics and Geotechnical Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1674775520301384 |
| _version_ | 1818942600572305408 |
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| author | Yared W. Bekele |
| author_facet | Yared W. Bekele |
| author_sort | Yared W. Bekele |
| collection | DOAJ |
| description | Neural networks with physical governing equations as constraints have recently created a new trend in machine learning research. In this context, a review of related research is first presented and discussed. The potential offered by such physics-informed deep learning models for computations in geomechanics is demonstrated by application to one-dimensional (1D) consolidation. The governing equation for 1D problems is applied as a constraint in the deep learning model. The deep learning model relies on automatic differentiation for applying the governing equation as a constraint, based on the mathematical approximations established by the neural network. The total loss is measured as a combination of the training loss (based on analytical and model predicted solutions) and the constraint loss (a requirement to satisfy the governing equation). Two classes of problems are considered: forward and inverse problems. The forward problems demonstrate the performance of a physically constrained neural network model in predicting solutions for 1D consolidation problems. Inverse problems show prediction of the coefficient of consolidation. Terzaghi’s problem, with varying boundary conditions, is used as a numerical example and the deep learning model shows a remarkable performance in both the forward and inverse problems. While the application demonstrated here is a simple 1D consolidation problem, such a deep learning model integrated with a physical law has significant implications for use in, such as, faster real-time numerical prediction for digital twins, numerical model reproducibility and constitutive model parameter optimization. |
| first_indexed | 2024-12-20T07:14:01Z |
| format | Article |
| id | doaj.art-9f25c69d4ce347f6a18c0fa777fca04f |
| institution | Directory Open Access Journal |
| issn | 1674-7755 |
| language | English |
| last_indexed | 2024-12-20T07:14:01Z |
| publishDate | 2021-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Rock Mechanics and Geotechnical Engineering |
| spelling | doaj.art-9f25c69d4ce347f6a18c0fa777fca04f2022-12-21T19:48:50ZengElsevierJournal of Rock Mechanics and Geotechnical Engineering1674-77552021-04-01132420430Physics-informed deep learning for one-dimensional consolidationYared W. Bekele0Rock and Soil Mechanics Group, SINTEF AS, Trondheim, NorwayNeural networks with physical governing equations as constraints have recently created a new trend in machine learning research. In this context, a review of related research is first presented and discussed. The potential offered by such physics-informed deep learning models for computations in geomechanics is demonstrated by application to one-dimensional (1D) consolidation. The governing equation for 1D problems is applied as a constraint in the deep learning model. The deep learning model relies on automatic differentiation for applying the governing equation as a constraint, based on the mathematical approximations established by the neural network. The total loss is measured as a combination of the training loss (based on analytical and model predicted solutions) and the constraint loss (a requirement to satisfy the governing equation). Two classes of problems are considered: forward and inverse problems. The forward problems demonstrate the performance of a physically constrained neural network model in predicting solutions for 1D consolidation problems. Inverse problems show prediction of the coefficient of consolidation. Terzaghi’s problem, with varying boundary conditions, is used as a numerical example and the deep learning model shows a remarkable performance in both the forward and inverse problems. While the application demonstrated here is a simple 1D consolidation problem, such a deep learning model integrated with a physical law has significant implications for use in, such as, faster real-time numerical prediction for digital twins, numerical model reproducibility and constitutive model parameter optimization.http://www.sciencedirect.com/science/article/pii/S1674775520301384Physics-informed deep learningConsolidationForward problemsInverse problems |
| spellingShingle | Yared W. Bekele Physics-informed deep learning for one-dimensional consolidation Journal of Rock Mechanics and Geotechnical Engineering Physics-informed deep learning Consolidation Forward problems Inverse problems |
| title | Physics-informed deep learning for one-dimensional consolidation |
| title_full | Physics-informed deep learning for one-dimensional consolidation |
| title_fullStr | Physics-informed deep learning for one-dimensional consolidation |
| title_full_unstemmed | Physics-informed deep learning for one-dimensional consolidation |
| title_short | Physics-informed deep learning for one-dimensional consolidation |
| title_sort | physics informed deep learning for one dimensional consolidation |
| topic | Physics-informed deep learning Consolidation Forward problems Inverse problems |
| url | http://www.sciencedirect.com/science/article/pii/S1674775520301384 |
| work_keys_str_mv | AT yaredwbekele physicsinformeddeeplearningforonedimensionalconsolidation |