Supercritical carbon dioxide critical flow model based on a physics-informed neural network

The venting of supercritical carbon dioxide (SCO2) involves trans-critical depressurization and multiphase phenomena, challenging the development of accurate and efficient critical flow models with limited data. Physics-informed Neural Networks (PINNs) incorporate physical constraints to solve complex problems with sparse data while retaining the efficiency of traditional neural networks. However, their application to SCO2 critical flow prediction remains unexplored, and an effective constraint paradigm is undefined. This study develops a high-precision PINN model for SCO2 critical flow prediction within an optimized physical constraint framework. Starting with a purely data-driven Recurrent Neural Network (RNN) model, the study examines two physical constraint types (P1 and P2) and different integration methods: embedding constraints in the loss function as soft constraints (M1) and incorporating them into the grid structure as hard constraints (M2). The optimal paradigm is identified by evaluating generalization, interpretability, and efficiency across datasets. The best PINN model, M1P1, reduces average prediction error by 48.67 %, 19.48 %, and 22.82 % compared to numerical, empirical, and data-driven models, respectively. M1P1 maintains comparable computational efficiency to empirical and data-driven models while surpassing numerical methods by four orders of magnitude, offering a precise and efficient SCO2 critical flow solution based on sparse data.