Multi-Constitutive Neural Network for Large Deformation Poromechanics Problem

TL;DR

The paper tackles large-strain poromechanics with multiple constitutive laws by introducing the Multi-Constitutive Neural Network (MCNN), which encodes the selected law as a one-hot input alongside $(\hat{X}, \hat{t})$ to predict the solution $J$ in a single model. By enforcing the governing PDEs through automatic differentiation and combining law-specific residuals with a one-hot weighting, MCNN trains simultaneously for all constitutive laws and can outperform independently trained PINNs in some cases. The approach demonstrates accurate predictions of pore pressure and settlement across three hyper-elastic laws, highlighting improved data efficiency and cross-law information transfer. This framework has potential impact for reservoir, geothermal, and geomechanics applications where multiple constitutive behaviors arise within a single problem domain.

Abstract

In this paper, we study the problem of large-strain consolidation in poromechanics with deep neural networks (DNN). Given different material properties and different loading conditions, the goal is to predict pore pressure and settlement. We propose a novel method "multi-constitutive neural network" (MCNN) such that one model can solve several different constitutive laws. We introduce a one-hot encoding vector as an additional input vector, which is used to label the constitutive law we wish to solve. Then we build a DNN which takes $(\hat{X}, \hat{t})$ as input along with a constitutive law label and outputs the corresponding solution. It is the first time, to our knowledge, that we can evaluate multi-constitutive laws through only one training process while still obtaining good accuracies. We found that MCNN trained to solve multiple PDEs outperforms individual neural network solvers trained with PDE in some cases.

Figures (3)

• Figure 1: A schematic diagram of our proposed MCNN. The inputs (left) include $\hat{X}$, $t$ and the law encoding vector $\vec{e}$. The $\sigma$ in the neural network represents the activation function; weights and biases are not shown for simplicity. Time and spatial derivatives of $J$ for the PDE formulations are computed through AD Baydin2017Xu2020Huang2020.
• Figure 2: Plots of predicted $J$ with MCNN and FD. MCNN is able to make an accurate inference for each constitutive law.
• Figure 3: A visualization of MCNN predictions and reference solutions for the dimensionless settlement $\hat{U}$. Predictions from MCNN, even though they are generated by the same model, are very accurate for all three constitutive laws.