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

TL;DR

This paper introduces a novel VPINN method for solving parabolic PDEs, specifically applied to heat conduction in industrial processes, combining time discretization with residual minimization, validated on a thermal dynamics case.

Contribution

It presents a new VPINN framework integrating time discretization and residual minimization for parabolic PDEs, validated on industrial heat conduction modeling.

Findings

Successfully modeled thermal dynamics of coffee extract freezing.

Accurately captured temperature-dependent properties and experimental data.

Validated the effectiveness of the VPINN approach for industrial heat transfer.

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.