Duhamel Neural Operator for Learning Phase-Field Dynamics

Phase-field simulators are used to predict how polarization fields evolve, a task that has been challenging due to their high computational cost. Machine learning surrogates have quicker inference times, but tend to struggle in approximating the amplification of incubation noise. We introduce the Duhamel Neural Operator (Duhamel-NO), a neural operator architecture consisting of a Fourier state-space model and a next-step U-Shaped Neural Operator, whose update is built on Duhamel’s principle applied to the Time-Dependent Ginzburg–Landau (TDGL) theory. Duhamel-NO reproduces the reference solver’s (FERROX) trajectories up to three orders of magnitude faster while exhibiting the most physically consistent predictions and significantly lower error than the best of seven tuned baselines, achieving a near-perfect correlation zero-shot generalization on unseen materials, initializations, and free energy landscapes. Additionally, we construct an open benchmark for ferroelectric phase-field dynamics.