Simulating the Cahn–Hilliard–Hele–Shaw system via a deep neural operator framework

The Cahn–Hilliard–Hele–Shaw (CHHS) system is a classical model for simulating interfacial dynamics in multiphysics problems. However, conventional numerical solvers often suffer from high computational costs due to the system’s nonlinear and multiscale characteristics. Recent advances in deep learning offer promising alternatives for solving partial differential equations with improved efficiency. In this work, we systematically evaluate a range of neural operator architectures, including convolutional, spectral, and attention-based designs, to simulate the CHHS system with enhanced efficiency and accuracy. These models are assessed on three representative datasets that capture distinct physical processes of the CHHS system, including interface evolution, interface break-up, and buoyancy-driven flow. The results show that the deep neural operator framework is highly effective in modeling complex interfacial dynamics. The UNO model, which incorporates spectral features and multiscale mechanisms, demonstrates enhanced accuracy and efficiency.