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arXiv · 2312.05410

Rethinking materials simulations: Blending direct numerical simulations with neural operators

Vivek Oommen·Khemraj Shukla·Saaketh Desai·Remi Dingreville·George Em Karniadakis
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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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Vivek Oommen, Khemraj Shukla, Saaketh Desai, Remi Dingreville, George Em Karniadakis. 2023-12-08. Rethinking materials simulations: Blending direct numerical simulations with neural operators. https://arxiv.org/abs/2312.05410

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