Reconstruction of the pressure field in dense granular flow using physics-informed neural network

Granular flows are extensively witnessed in natural environments such as dunes in deserts and avalanches, and industrial applications such as transporting cement and grains. Measuring the inherent pressure fields is usually challenging in such flows. In this work, we utilize the physics-informed neural networks that solve the inverse problem of reconstructing the pressure field of granular materials using the data of velocity fields. The proposed Physics-Informed Neural Network for Modeling Granular Flow (GF-PINN) incorporates the Navier–Stokes equation and the μ(I) rheology of dense granular materials, and deploys a regularization parameter λ to circumvent the divergence of the model. The results show that the GF-PINN enables the reconstruction of the pressure fields based solely on the velocity fields, with the L2 norm error of the reconstructed pressure field less than 10% under various configurations. Furthermore, GF-PINN can infer key material parameters of the μ(I) rheology directly from the field flow with an error range of less than 6%. In addition, the GF-PINN maintains good accuracy of pressure prediction until the noise intensity of velocity fields increases up to 0.5.