Deep Ritz Neural Operator for Dendritic Growth via Energy Splitting

We propose a neural operator approach bridging classical convex-concave splitting with physics-informed learning to accelerate phase-field simulations. By training via an energy-splitting variational formulation, we enforce the energy dissipation property of the underlying models. We further introduce a Reaction-Diffusion Neural Operator architecture, specifically designed to incorporate the operator-splitting of diffusion and reaction terms in the model equation. For the anisotropic dendritic growth simulation, we show that our approach provides better generalization and higher accuracy than the data-driven training approach, while achieving faster inference than traditional Fourier spectral methods.