Accelerating Phase Field Modeling Through Hybrid Simulations using Fourier Neural Operators and UNets
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Computational simulation of phase field dynamics can be prohibitively expensive when using standard numerical solvers. For example, high-fidelity simulations often use very small time steps due to stability considerations, which can become a bottleneck when the target quantities of interest require predictions over long time horizons. To address this challenge, we employ machine learning-based surrogate models to help extrapolate forward in time, enabling predictions at time scales far beyond what is achievable through traditional methods alone. Specifically, we investigate two deep learning architectures, Fourier Neural Operators (FNOs) and UNets. We train them to predict a later time step given an earlier one, but with a much coarser time stepping than the high-fidelity simulation – thus encapsulating multiple high-fidelity steps within a single surrogate evaluation. While this approach enables more rapid predictions through autoregressive evaluation of the surrogate, the incurred error is essentially uncontrolled. To alleviate this, we adopt a hybrid prediction strategy which alternates between surrogate evaluations – which leap forward in time – and high fidelity simulation steps – which reduce errors and bring the system state back to the solution manifold. Moreover, we show that including periodic retraining or online fine-tuning can provide further control on the error growth. We illustrate these methods on two examples, a simpler Cahn-Hilliard system and a more sophisticated liquid metal dealloying simulation.
