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

arXiv: https://arxiv.org/abs/2201.13389 · HTML: https://mlsanity.com/paper/2201.13389/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 21 of 21)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Parallel Physics-Informed Neural Networks via Domain Decomposition](https://mlsanity.com/paper/2104.10013/) (2021)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport](https://mlsanity.com/paper/1912.02968/) (2019)
- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework](https://mlsanity.com/paper/2012.07938/) (2020)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions](https://mlsanity.com/paper/2105.09513/) (2021)
- [Learning Unknown Physics of non-Newtonian Fluids](https://mlsanity.com/paper/2009.01658/) (2020)
- [Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks](https://mlsanity.com/paper/1909.12228/) (2019)

## Built on by (most cited first, 6 of 6)

- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [Fixed-budget online adaptive learning for physics-informed neural networks. Towards parameterized problem inference](https://mlsanity.com/paper/2212.11776/) (2022)
- [Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers](https://mlsanity.com/paper/2512.09202/) (2025)
- [Geometry-aware framework for deep energy method: an application to structural mechanics with hyperelastic materials](https://mlsanity.com/paper/2405.03427/) (2024)
- [Enhancing Nuclear Reactor Core Simulation through Data-Based Surrogate Models](https://mlsanity.com/paper/2511.16148/) (2025)
- [Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order models](https://mlsanity.com/paper/2608.03360/) (2026)

## Abstract (arXiv)

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.