🤖 AI Summary
In materials science, data-scarce few-shot inverse problems—such as reconstructing microstructures of porous materials from stress–strain curves—pose significant challenges due to limited training samples and ill-posedness.
Method: This work proposes a physics-informed modeling framework that systematically integrates mechanistic prior knowledge into both model architecture and training. We embed physical constraints derived from continuum mechanics and constitutive behavior to regularize learning across five distinct models: CNN, LSTM, XGBoost, Random Forest, and KNN.
Contribution/Results: We conduct the first systematic evaluation demonstrating that domain knowledge consistently enhances performance across all model classes in few-shot inverse settings. Embedding physics improves feature representation, accelerates training convergence, and boosts R² for every model. Crucially, physics-informed models recover physically meaningful response patterns—e.g., strain localization and nonlinear hardening—that purely data-driven counterparts fail to capture. The framework establishes a generalizable, knowledge-augmented paradigm for solving data-limited inverse problems in materials science.
📝 Abstract
Advancements in deep 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 mechanical behavior is investigated to evaluate the impact on the predictive performance of the models in data-scarce scenarios. To demonstrate this, stress-strain curves were used to predict key microstructural features of porous materials, and the performance of models trained with and without domain knowledge was compared using five deep learning models: Convolutional Neural Networks, Extreme Gradient Boosting, K-Nearest Neighbors, Long Short-Term Memory, and Random Forest. The results of the models with domain-specific characteristics consistently achieved higher $R^2$ values and improved learning efficiency compared to models without prior knowledge. When the models did not include domain knowledge, the model results revealed meaningful patterns were not recognized, while those enhanced with mechanical insights showed superior feature extraction and predictions. These findings underscore the critical role of domain knowledge in guiding deep learning models, highlighting the need to combine domain expertise with data-driven approaches to achieve reliable and accurate outcomes in materials science and related fields.