Towards long rollout of neural operators with local attention and flow matching-inspired correction: An example in frontal polymerization PDEs

Recent advances in frontal ring-opening metathesis polymerization (FROMP) offer a sustainable energy-efficient alternative for the rapid curing of thermoset polymers. Predicting the dynamics and spontaneous patterning of FROMP require numerically solving reaction-diffusion PDEs but it is computationally expensive. Neural operators serve as surrogate PDE solvers but face challenges in long temporal rollouts. Herein, we augment Fourier neural operators with large kernel attention to better learn local instabilities in FROMP. Inspired by conditional functional flow matching, we proposed a correction scheme to refine neural PDE predictions to extend rollout accuracies. Our work paves a step forward in predicting long-term dynamics of FROMP and other complex time-dependent PDEs.