Towards spatio-temporal extrapolation of phase-field simulations with convolution-only neural networks

Phase-field simulations of liquid metal dealloying (LMD) capture complex microstructural evolution but become prohibitively expensive over large domains and long time horizons. We introduce a fully convolutional, conditionally parameterized U-Net surrogate designed to extrapolate far beyond its training data in both space and time. The architecture combines convolutional self-attention, physically informed padding, and a flood-fill corrector to preserve accuracy under extrapolation, while conditioning on simulation parameters enables flexible time-step skipping and adaptation to varying alloy compositions. To eliminate the need for costly solver-based initialization, we couple the surrogate with a conditional diffusion model that generates synthetic, physically consistent initial conditions. Training uses simulations on small domains over short time spans; exploiting the convolutional nature of U-Nets, the trained surrogate then runs and extrapolates to longer horizons than classical numerical solvers can reach. Across multiple alloy compositions, the framework reproduces LMD physics accurately within the spatial and temporal ranges validated against direct numerical simulation (DNS). It predicts key quantities of interest and spatial statistics with relative errors typically below 5% in the training regime and under 15% during large-scale, long-horizon extrapolation. The framework delivers speed-ups of O(10⁴) over DNS, reducing weeks-long simulations to seconds and allowing the computational domain to expand beyond what conventional mesh-based discretizations permit. This work is a first stepping stone toward surrogate models for rapid screening, parameter studies, and uncertainty quantification in LMD.