Learning Latent Hardening (LLH): Enhancing Deep Learning with Domain Knowledge for Material Inverse Problems

TL;DR

The paper tackles inverse material problems under data scarcity by introducing Learning Latent Hardening (LLH), a two-step framework that first reconstructs full stress-strain curves from partial data using a tailored fully connected DNN and then predicts four Minkowski-functionals $M_0$–$M_3$ describing microstructure from the reconstructed curves. It demonstrates that incorporating domain knowledge, including a Hadwiger-based strength law, improves predictive accuracy across multiple models (CNN, KNN, LSTM, RF, XGBoost), achieving test $R^2$ values around $0.985$ for reconstruction and up to $0.9936$ for microstructure prediction. The study highlights the value of integrating physical priors with DL/ML in data-scarce inverse problems, enabling robust reconstruction of mechanical behavior and accurate inference of porous-material microstructure. This approach has potential impact for geomechanics and material design by enabling reliable material characterization from partial measurements.

Abstract

Advancements in deep learning and machine learning have improved the ability to model complex, nonlinear relationships, such as those encountered in complex material inverse problems. However, the effectiveness of these methods often depends on large datasets, which are not always available. In this study, the incorporation of domain-specific knowledge of the mechanical behavior of material microstructures is investigated to evaluate the impact on the predictive performance of the models in data-scarce scenarios. To overcome data limitations, a two-step framework, Learning Latent Hardening (LLH), is proposed. In the first step of LLH, a Deep Neural Network is employed to reconstruct full stress-strain curves from randomly selected portions of the stress-strain curves to capture the latent mechanical response of a material based on key microstructural features. In the second step of LLH, the results of the reconstructed stress-strain curves are leveraged to predict key microstructural features of porous materials. The performance of six deep learning and/or machine learning models trained with and without domain knowledge are compared: Convolutional Neural Networks, Deep Neural Networks, Extreme Gradient Boosting, K-Nearest Neighbors, Long Short-Term Memory, and Random Forest. The results from the models with domain-specific information consistently achieved higher $R^2$ values compared to models without prior knowledge. Models without domain knowledge missed critical patterns linking stress-strain behavior to microstructural changes, whereas domain-informed models better identified essential stress-strain features predictive of microstructure. These findings highlight the importance of integrating domain-specific knowledge with deep learning to achieve accurate outcomes in materials science.

Figures (11)

• Figure 1: Five randomly selected examples of stress-strain curve results from the 654 different microstructures peloquin2023neuralLindqwister2023: (a) original data and (b) masked partial data.
• Figure 2: Original data before outliers were removed: (a) porosity; (b) surface area; (c) mean curvature; (d) Euler characteristic.
• Figure 3: Example microstructure peloquin2023neural to generate stress-strain curves in previous work Lindqwister2023 and images showing each of the four main functionals used in this work.
• Figure 4: The architecture of the LLH workflow model.
• Figure 5: Representative test data and results comparing the ground truth, masked training data, and predicted (DNN-reconstructed) stress-strain curves.