# Learning rheological parameters of non-Newtonian fluids from velocimetry data

arXiv: https://arxiv.org/abs/2408.02604 · HTML: https://mlsanity.com/paper/2408.02604/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 5 Aug 2024.

## Builds on (most cited first, 3 of 3)

- [Practical Quasi-Newton Methods for Training Deep Neural Networks](https://mlsanity.com/paper/2006.08877/) (2020)
- [Joint reconstruction and segmentation of noisy velocity images as an inverse Navier-Stokes problem](https://mlsanity.com/paper/2207.01368/) (2022)
- [Bayesian inverse Navier-Stokes problems: joint flow field reconstruction and parameter learning](https://mlsanity.com/paper/2406.18464/) (2024)

## Abstract (arXiv)

We solve a Bayesian inverse Navier-Stokes (N-S) problem that assimilates velocimetry data in order to jointly reconstruct the flow field and learn the unknown N-S parameters. By incorporating a Carreau shear-thinning viscosity model into the N-S problem, we devise an algorithm that learns the most likely Carreau parameters of a shear-thinning fluid, and estimates their uncertainties, from velocimetry data alone. We then conduct a flow-MRI experiment to obtain velocimetry data of an axisymmetric laminar jet through an idealised medical device (FDA nozzle) for a blood analogue fluid. We show that the algorithm can successfully reconstruct the flow field by learning the most likely Carreau parameters, and that the learned parameters are in very good agreement with rheometry measurements. The algorithm accepts any algebraic effective viscosity model, as long as the model is differentiable, and it can be extended to more complicated non-Newtonian fluids (e.g. Oldroyd-B fluid) if a viscoelastic model is incorporated into the N-S problem.