Rethinking materials simulations: Blending direct numerical simulations with neural operators

• URL: http://arxiv.org/abs/2312.05410v1
• Date: Fri, 8 Dec 2023 23:44:54 GMT
• Title: Rethinking materials simulations: Blending direct numerical simulations with neural operators
• Authors: Vivek Oommen, Khemraj Shukla, Saaketh Desai, Remi Dingreville, George Em Karniadakis
• Abstract summary: We develop a new method that blends numerical solvers with neural operators to accelerate such simulations. We demonstrate the effectiveness of this framework on simulations of microstructure evolution during physical vapor deposition.
• Score: 1.6874375111244329
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Direct numerical simulations (DNS) are accurate but computationally expensive for predicting materials evolution across timescales, due to the complexity of the underlying evolution equations, the nature of multiscale spatio-temporal interactions, and the need to reach long-time integration. We develop a new method that blends 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 that enables accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this framework on simulations of microstructure evolution during physical vapor deposition modeled via the phase-field method. Such simulations exhibit high spatial gradients due to the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with up to 16.5$\times$ speed-up compared to DNS. This methodology is generalizable to a broad range of evolutionary models, from solid mechanics, to fluid dynamics, geophysics, climate, and more.

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