DeepRitzSplit Neural Operator for Phase-Field Models via Energy Splitting

• URL: http://arxiv.org/abs/2604.18261v1
• Date: Mon, 20 Apr 2026 13:34:50 GMT
• Title: DeepRitzSplit Neural Operator for Phase-Field Models via Energy Splitting
• Abstract summary: We propose a new neural operator approach that bridges classical convex-concave splitting schemes with physics-informed learning.<n>It consists of a Deep Ritz method, where a neural operator is trained to approximate a variational formulation of the phase-field model.<n>We successfully apply the deep learning approach to the isotropic Allen-Cahn equation and to anisotropic dendritic growth simulation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The multi-scale and non-linear nature of phase-field models of solidification requires fine spatial and temporal discretization, leading to long computation times. This could be overcome with artificial-intelligence approaches. Surrogate models based on neural operators could have a lower computational cost than conventional numerical discretization methods. We propose a new neural operator approach that bridges classical convex-concave splitting schemes with physics-informed learning to accelerate the simulation of phase-field models. It consists of a Deep Ritz method, where a neural operator is trained to approximate a variational formulation of the phase-field model. By training the neural operator with an energy-splitting variational formulation, we enforce the energy dissipation property of the underlying models. We further introduce a custom Reaction-Diffusion Neural Operator (RDNO) architecture, adapted to the operators of the model equations. We successfully apply the deep learning approach to the isotropic Allen-Cahn equation and to anisotropic dendritic growth simulation. We demonstrate that our physically-informed training provides better generalization in out-of-distribution evaluations than data-driven training, while achieving faster inference than traditional Fourier spectral methods.

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