Improving the one-dimensional interfacial area transport equation using a physics-informed machine learning method

Abstract

The interfacial area concentration modeling has been greatly improved with the development of the interfacial area transport equation (IATE). The one-dimensional IATE, which is obtained through area-averaging the three-dimensional form of the model, has been adopted into many thermal hydraulic analysis codes. Towards improving the performance of one dimensional interfacial area transport equation, along with many of the existing studies on developing sophisticated source and sink constitutive models describing the liquid-bubble and bubble-bubble interactions, additional efforts should be made on improving the accuracies of the closure models supporting the calculation of these constitutive models. In this study, a physics-informed machine learning method was proposed that couples the machine learning and the IATE model for improving the performance of the existing IATE models. The machine learning model serves to predict the errors of the closure models that calculate the key parameters related to the interfacial area transports. The machine learning model is guided by the physical models, and its training is through an IATE model-based loss optimization. To effectively train the machine learning model, a data augmentation method was developed based on the existing IAC database. The newly proposed method that couples the trained machine learning model and the IATE model gives a 12% of improvement compared with the state-of-art IATE model. This new method and the approach on training the model provide good reference on how to effectively couple the machine learning and physical model for an improved modeling of the indirectly observable physical phenomena.