Materials 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.

基于直接数值求解器的材料模拟是准确的，但由于基础演化方程的复杂性、多尺度时空相互作用的性质以及实现长时间积分的需要，预测材料在长度和时间尺度上的演化时计算成本昂贵。我们开发了一种将直接数值求解器与神经算子相结合的方法，以加速此类模拟。该方法基于社区数值求解器与 U-Net 神经算子的集成，并通过时间条件机制进行增强，以实现准确的外推和有效的动力学求解时间预测。我们证明了这种混合框架通过相场方法模拟微观结构演化的有效性。这种模拟表现出高空间梯度和不同材料相的共同演化，同时具有慢速和快速的材料动力学。根据所使用的混合策略，我们建立了耦合求解器的准确外推法，与 DNS 相比具有较大的加速。这种方法可推广到广泛的材料模拟，从固体力学到流体动力学、地球物理学、气候等等。