Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone
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| Autores principales: | , , , , , , |
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2024
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| author | Bonneville, Christophe Bieberdorf, Nathan Hegde, Arun Asta, Mark Najm, Habib N. Capolungo, Laurent Safta, Cosmin |
| author_facet | Bonneville, Christophe Bieberdorf, Nathan Hegde, Arun Asta, Mark Najm, Habib N. Capolungo, Laurent Safta, Cosmin |
| contents | Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, stiffness in the PDEs requires an extremely small time steps (e.g. $10^{-12}$ 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 U-Shaped Adaptive Fourier Neural Operators (U-AFNO), a machine learning (ML) 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 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) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in-spite of the chaotic nature of LMD. Our model reproduces the key micro-structure statistics and QoIs with a level of accuracy on-par with the high-fidelity numerical solver. We also investigate the opportunity of using hybrid simulations, in which we alternate forward leap 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone Bonneville, Christophe Bieberdorf, Nathan Hegde, Arun Asta, Mark Najm, Habib N. Capolungo, Laurent Safta, Cosmin Computational Engineering, Finance, and Science Computer Vision and Pattern Recognition Machine Learning Numerical Analysis Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, stiffness in the PDEs requires an extremely small time steps (e.g. $10^{-12}$ 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 U-Shaped Adaptive Fourier Neural Operators (U-AFNO), a machine learning (ML) 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 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) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in-spite of the chaotic nature of LMD. Our model reproduces the key micro-structure statistics and QoIs with a level of accuracy on-par with the high-fidelity numerical solver. We also investigate the opportunity of using hybrid simulations, in which we alternate forward leap 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. |
| title | Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone |
| topic | Computational Engineering, Finance, and Science Computer Vision and Pattern Recognition Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2406.17119 |