Direct numerical simulation of natural convection based on parameter-input physics-informed neural networks

Thermal convection is frequently observed in nature and widely used in industry, making it an important subject for many experimental and numerical studies. A well-researched paradigm for comprehending thermal convection is the system of thermally driven square cavities, one of the classical problems of natural convection. With the development of computational resources, methods for solving natural convection problems using deep learning techniques have flourished. In this study, a Physics-informed neural networks (PINNs) method is used to solve the thermal convection problem, with neural networks trained to simulate the velocity and temperature fields of natural convection at various Ra numbers ranging from $Ra={10}^3$ to $Ra={10}^8$. Furthermore, a parameter-input PINNs model is constructed to further develop this approach. This framework has the advantage of concurrently and rapidly predicting the flow field outcomes for any Ra number scenario in the specified range. Additionally, the flow field outcomes of the parameter-input PINNs model are statistically analyzed to demonstrate the model’s generalization performance.