Proximal Splitting Methods for Hybrid Differentiable Models

Operator splitting methods are at the foundation of many numerical solvers for partial differential equations. In parallel, unrolled and hybrid learning-based architectures have been introduced to enhance classical solvers, but their design is rarely linked to the underlying problem structure. In this work, we propose a unifying framework that explicitly links operator splitting algorithms from optimization with unrolled hybrid architectures. We show that each operator splitting scheme naturally defines an unrolled architecture, which recovers a wide range of existing plug-and-play and hybrid models as special cases. Using this framework, we design new unrolled hybrid architectures and validate them on benchmark fluid dynamics simulations, where they achieve improved accuracy and stability.