A Differentiable Hybrid Neural Solver for Efficient Simulation of Cavitating Flows*

Cavitation is a prevalent phenomenon in nature and engineering, leading to erosion, noise, and efficiency loss in hydraulic machines. However, the computational costs of conventional numerical solvers for such multi-physics, multi-scale simulations are prohibitively high. To address this challenge and leverage the advances in machine learning and ever-increasing data availability, we present a novel differentiable programming approach that merges machine learning with classical numerical solvers to achieve efficient GPU-accelerated simulation of cavitating flows. Specifically, we develop a differentiable hybrid neural solver, which employs a homogeneous equilibrium model with a barotropic correlation to accurately model cavitation. Since all the modules are coded on JAX with auto-differentiation capabilities, gradient can be back-propagated over the entire model, allowing a seamless integration with neural networks, which can be trained in an end-to-end, sequence-to-sequence manner. The excellent performance of the proposed neural differentiable modeling is exhibited as compared against pure data-driven model and traditional numerical solver.