Rethinking materials simulations: Blending direct numerical simulations with neural operators - Link

Abstract

Materials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and timescales, 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.

Architecture: UNet with temporal-conditioning

Test trajectories predicted by the Hybrid Model (Speedup 2.27x)

1) Physical Vapour Deposition

2) Dendritic Microstructures

3) Spinodal Decomposition

Citation

@article{oommen2024rethinking,
  title={Rethinking materials simulations: Blending direct numerical simulations with neural operators},
  author={Oommen, Vivek and Shukla, Khemraj and Desai, Saaketh and Dingreville, R{\'e}mi and Karniadakis, George Em},
  journal={npj Computational Materials},
  volume={10},
  number={1},
  pages={145},
  year={2024},
  publisher={Nature Publishing Group UK London}
}