Application of physics-informed neural networks for thin liquid film flows

The flow of a film induced by gravity is not only widespread in nature but also has significant applications in various industrial technologies such as coating techniques, nanotechnology, microfluidic chips, and heat exchangers. The film exhibits various nonlinear dynamic phenomena due to the interactions between surface tension, gravity, and other forces, making the study of this type of flow of great importance. However, the theoretical derivation of thin film fluid dynamics is complex, with diverse working conditions, making numerical solutions difficult, time-consuming, and labor-intensive. Therefore, it is of significant importance to seek an approach that differs from theoretical derivation or numerical solutions for the study of thin film fluid dynamics. With the rapid development of deep learning, this paper employs physics-informed neural networks (PINNs) algorithm, in conjunction with the partial differential equation governing the fluid film thickness, to conduct research on forward prediction of the film thickness variation over time and space, and inverse problem solving to determine unknown parameters in the governing equation from data. The study investigates the governing equation for the thickness of a falling film along an inclined plane and applies the PINNs method to solve it. The research predicted the film thickness for three different characteristic waveforms and conducted a comparative analysis with solutions obtained using the commercial software COMSOL. Additionally, the unknown parameters in the governing equation were inversely solved using limited data, and the differences in prediction results with and without noisy data were compared.