# Learning Unknown Physics of non-Newtonian Fluids

arXiv: https://arxiv.org/abs/2009.01658 · HTML: https://mlsanity.com/paper/2009.01658/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2020.

## Built on by (most cited first, 13 of 13)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
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- [Physics-constrained deep neural network method for estimating parameters in a redox flow battery](https://mlsanity.com/paper/2106.11451/) (2021)
- [Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media](https://mlsanity.com/paper/2203.01514/) (2022)
- [A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes](https://mlsanity.com/paper/2305.03184/) (2023)
- [Physics-informed neural networks for non-Newtonian fluid thermo-mechanical problems: an application to rubber calendering process](https://mlsanity.com/paper/2201.13389/) (2022)
- [A Tutorial on the Use of Physics-Informed Neural Networks to Compute the Spectrum of Quantum Systems](https://mlsanity.com/paper/2407.20669/) (2024)
- [Training Deep Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.23501/) (2025)
- [An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks](https://mlsanity.com/paper/2606.10686/) (2026)

## Abstract (arXiv)

We extend the physics-informed neural network (PINN) method to learn viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) using only velocity measurements. The PINN-inferred viscosity models agree with the empirical models for shear rates with large absolute values but deviate for shear rates near zero where the analytical models have an unphysical singularity. Once a viscosity model is learned, we use the PINN method to solve the momentum conservation equation for non-Newtonian fluid flow using only the boundary conditions.