Transfer learning and pretraining enhanced physics-informed machine learning for closed-circuit reverse osmosis modeling

Closed-circuit reverse osmosis (CCRO) is a widely concerned batch-type desalination process that exhibits dynamic, multi-mode, and cyclic behavior. This study provides a novel physics-informed machine learning method that integrate pretraining and transfer learning (PT-TL) to construct spatiotemporal model of the CCRO process. In this model, two types of networks are specifically tailored to approximate the latent solutions of the closedcircuit and flushing modes within each running cycle. To facilitate long-time integration of partial differential equations in the closed-circuit mode, time-adaptive decomposition is utilized in parameter transfer learning to identify appropriate sequence partitioning and accelerate the learning process. During the pretraining step, a coarse-grained model is constructed by adjusting the linear initial conditions of the flushing mode to capture time-varying characteristics. The integration of PT-TL with physics-informed machine learning not only reduces training time by over 50 % but also demonstrates comparable predictive ability to traditional numerical methods.