Physics-Informed Deep Learning for Industrial Processes: Time-Discrete VPINNs for heat conduction

Abstract: Neural networks offer powerful tools to solve partial differential equations (PDEs). We present a Variational Physics-Informed Neural Network (VPINN) designed for parabolic problems. Our approach combines a classical time discretization with a composed loss function, which minimizes the residual's dual norm at every time step. We validate the framework by modeling the freezing of coffee extracts in an industrial cylinder. The simulation accounts for temperature-dependent properties and experimental data. It successfully captures the thermal dynamics of the process.