Abstract
AbstractMaterials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and time-scales, due to the complexity of the underlying evolution equations, the nature of multiscale spatiotemporal interactions, and the need to reach long-time integration. We develop a method that blends direct numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism to enable accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this hybrid framework on simulations of microstructure evolution via the phase-field method. Such simulations exhibit high spatial gradients and the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with large speed-up compared to DNS depending on the hybrid strategy utilized. This methodology is generalizable to a broad range of materials simulations, from solid mechanics to fluid dynamics, geophysics, climate, and more.
Funder
DOE | National Nuclear Security Administration
United States Department of Defense | United States Air Force | AFMC | Air Force Office of Scientific Research
Publisher
Springer Science and Business Media LLC
Reference77 articles.
1. Hughes, T. J.The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Courier Corporation, 2012).
2. Godunov, S. K. & Bohachevsky, I. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Matematičeskij Sb. 47, 271–306 (1959).
3. Eymard, R., Gallouët, T. & Herbin, R. Finite volume methods. Handb. Numer. Anal. 7, 713–1018 (2000).
4. Karniadakis, G. & Sherwin, S. J.Spectral/HP Element Methods for Computational Fluid Dynamics (Oxford University Press, USA, 2005).
5. Hornik, K., Stinchcombe, M. & White, H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Netw. 3, 551–560 (1990).
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献