Rheological Parameter Identification in Granular Materials Using Physics-Informed Neural Networks

TL;DR

This work implements physics-informed neural networks to identify granular rheology parameters from a simple granular-column collapse, focusing on the μ(I) constitutive law characterized by μ_s and μ_2 (with I_0 fixed at 0.3). By combining velocity observations with pressure data at the granular–air interface, the PINN accurately recovers μ_s and μ_2 and simultaneously reconstructs the pressure field, demonstrating a data-driven rheometry approach for granular materials. The method shows robust parameter identification under moderate noise and reveals limitations in high-noise or near-stagnation regions, while highlighting the potential to apply the framework to real experimental data and to broaden parameter identifiability by exploring additional flow configurations. Overall, this study provides a proof of concept that PINNs can fuse flow physics and accessible observations to infer granular rheology without specialized rheometric equipment, offering a pathway to practical, data-driven rheometry in granular systems.

Abstract

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising tool for fluid dynamics, particularly for flow reconstruction and parameter identification. In the context of granular media, accurately estimating rheological parameters remains a major challenge, as it typically requires complex and costly experimental setups. In this work, we propose a PINN-based approach to identify key rheological parameters of granular materials using a simple experiment: the granular column collapse. A proof of concept is presented using synthetic data, where the PINN is trained to infer the flow fields while simultaneously recovering the rheological parameters. Beyond parameter identification, the method also enables reconstruction of the pressure field, which is difficult to access experimentally. The results highlight the potential of PINNs for data-driven rheometry of granular materials and open perspectives for future applications with real experimental data.

Figures (7)

• Figure 1: Friction law $\mu(I)$ for different values of (a) $\mu_s$ (with $\mu_2=0.52$ and $I_0=0.3$) ; (b) $\mu_2$ (with $\mu_s=0.2$ and $I_0=0.3$) ; (c) $I_0$ (with $\mu_s=0.2$ and $\mu_2=0.52$).
• Figure 2: Collapse of a granular column: (a) sketch of the 2D configuration and prescribed boundary conditions during the collapse at the initial state and the final state; (b) images from the laboratory of a quasi-2D configuration from gans2023collapse.
• Figure 3: Final states of six numerical simulations of granular column collapses for different frictional parameters. The simulations are organized according to the values of $\mu_s$. The color maps represent the spatial distribution of $D_2$ within the resulting deposits.
• Figure 4: Physic informed neural network structure : a fully connected neural network take as input $\textrm{x}=(x,y,t) \in \mathbb{R}^{3}$ and predicts $\boldsymbol{\mathcal{N}}(\textrm{x}) = (u_{\mathcal{N}}(\textrm{x}),v_{\mathcal{N}}(\textrm{x}),p_{\mathcal{N}}(\textrm{x}))$. The residuals of the governing equations $e_{u,v}$ and $e_{\text{cont}}$ are computed by automatic differentiation and $e_0$ denotes the mismatch between the observational data ($u_\mathbf{x}$, $v_\mathbf{x}$, $p_{\text{surf},\mathbf{x}}$) and the ANN predictions, which are combined in the loss function $\mathcal{L}$. The trainable parameters ($\mu_s$, $\mu_2$) from the $\mu(I)$ rheology are initialized with the model, and their values are adjusted during training, similarly to the internal parameters $\Theta$ of the model.
• Figure 5: Evolution of the predicted value of (a) $\mu_s$ and (b) $\mu_2$ for the case of $\mu_s = 0.6$ and $\mu_2=0.84$.