Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone
Abstract Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | npj Computational Materials |
| Online Access: | https://doi.org/10.1038/s41524-024-01488-z |
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| author | Christophe Bonneville Nathan Bieberdorf Arun Hegde Mark Asta Habib N. Najm Laurent Capolungo Cosmin Safta |
| author_facet | Christophe Bonneville Nathan Bieberdorf Arun Hegde Mark Asta Habib N. Najm Laurent Capolungo Cosmin Safta |
| author_sort | Christophe Bonneville |
| collection | DOAJ |
| description | Abstract Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10−12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes. |
| format | Article |
| id | doaj-art-1bb2ffbf05bd487e9bf322fe17c28686 |
| institution | Kabale University |
| issn | 2057-3960 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Computational Materials |
| spelling | doaj-art-1bb2ffbf05bd487e9bf322fe17c286862025-01-19T12:32:29ZengNature Portfolionpj Computational Materials2057-39602025-01-0111111610.1038/s41524-024-01488-zAccelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backboneChristophe Bonneville0Nathan Bieberdorf1Arun Hegde2Mark Asta3Habib N. Najm4Laurent Capolungo5Cosmin Safta6Sandia National LaboratoriesMaterials Sciences Division, Lawrence Berkeley National LaboratorySandia National LaboratoriesMaterials Sciences Division, Lawrence Berkeley National LaboratorySandia National LaboratoriesLos Alamos National LaboratorySandia National LaboratoriesAbstract Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10−12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.https://doi.org/10.1038/s41524-024-01488-z |
| spellingShingle | Christophe Bonneville Nathan Bieberdorf Arun Hegde Mark Asta Habib N. Najm Laurent Capolungo Cosmin Safta Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone npj Computational Materials |
| title | Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone |
| title_full | Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone |
| title_fullStr | Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone |
| title_full_unstemmed | Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone |
| title_short | Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone |
| title_sort | accelerating phase field simulations through a hybrid adaptive fourier neural operator with u net backbone |
| url | https://doi.org/10.1038/s41524-024-01488-z |
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