Rethinking materials simulations: Blending direct numerical simulations
  with neural operators
Vivek Oommen Khemraj Shukla Saaketh Desai Remi Dingreville George Em Karniadakis
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.