Physics-informed neural networks for non-Newtonian fluid thermo-mechanical problems: an application to rubber calendering process

TL;DR

This paper demonstrates the effectiveness of Physics-Informed Neural Networks (PINNs) in solving complex non-Newtonian fluid thermo-mechanical problems, particularly in rubber calendering, including inverse, ill-posed, and noisy measurement scenarios.

Contribution

The study applies PINNs to a challenging industrial problem, showing their ability to infer hidden physical fields and unknown parameters from partial and noisy data, outperforming classical methods.

Findings

PINNs successfully estimate unknown parameters from sensor data.

PINNs can infer hidden physics in ill-posed boundary condition scenarios.

Sensor placement significantly affects PINNs performance.

Abstract

Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. However, the assessment of PINNs in industrial applications involving coupling between mechanical and thermal fields is still an active research topic. In this work, we present an application of PINNs to a non-Newtonian fluid thermo-mechanical problem which is often considered in the rubber calendering process. We demonstrate the effectiveness of PINNs when dealing with inverse and ill-posed problems, which are impractical to be solved by classical numerical discretization methods. We study the impact of the placement of the sensors and the distribution of unsupervised points on the performance of PINNs in a problem of inferring hidden physical fields from some partial data. We also investigate the capability of PINNs to identify unknown physical parameters from the measurements captured by sensors. The effect of noisy measurements is also considered throughout this work. The results of this paper demonstrate that in the problem of identification, PINNs can successfully estimate the unknown parameters using only the measurements on the sensors. In ill-posed problems where boundary conditions are not completely defined, even though the placement of the sensors and the distribution of unsupervised points have a great impact on PINNs performance, we show that the algorithm is able to infer the hidden physics from local measurements.