Combining U-Net and Neural Operator Models for Accelerating Phase-Field Simulations
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Computational simulation of phase field dynamics can be prohibitively expensive when using standard numerical solvers. 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 jump forward in time, enabling predictions at time horizons beyond what is achievable through traditional methods alone. Specifically, we investigate two deep learning architectures, Fourier Neural Operators (FNOs) and U-Nets, and train them to predict future states with much coarser time steps – 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 direct numerical simulation steps – which reduce errors and bring the system state back to the solution manifold. We illustrate these methods on phase-field simulations for a liquid metal dealloying system.