Fusing imbalanced data via Physical Condition-Aware Surrogate Modeling

Predicting material responses under diverse loading and boundary conditions is pivotal for understanding structure-property relationships and guiding material design. Traditional methods, such as physics-based simulations, often involve high computational costs, while experimental exploration across vast design spaces is impractical and resource-intensive. Convolutional Neural Networks (CNNs) have emerged as efficient tools for material response prediction, particularly for materials with intricate microstructures. However, these models face challenges stemming from imbalanced datasets, where critical material attributes such as displacement fields are less accessible and more expensive to obtain than others like strain energy. This imbalance can skew predictions and hinder the generalization of models to unseen material structures. To address these challenges, we propose a novel framework that integrates multi-task learning (MTL) with a Physical Conditions Informed Convolutional (PCIConv) layer to improve prediction accuracy and robustness under imbalanced data conditions. MTL enables the simultaneous prediction of multiple material responses, leveraging shared information across tasks to enhance model generalization. The inclusion of the PCIConv layer embeds physical insights into the learning process, further enhancing the model's adaptability to diverse conditions. We validate our approach using the Material MNIST dataset, demonstrating its ability to predict displacement fields and strain energy across various imbalance scenarios. Results show that the MTL framework, particularly when enhanced with PCIConv, outperforms single-task models by achieving superior accuracy and robustness, even with limited data for underrepresented attributes. This study highlights the potential of combining MTL and PCIConv in advancing material response predictions, offering a pathway to efficient and cost-effective material design while reducing reliance on computationally expensive simulations and experimental methods.