Constrained neural network training and its application to hyperelastic material modeling

Neural networks (NN) have been studied and used widely in the field of computational mechanics, especially to approximate material behavior. One of their disadvantages is the large amount of data needed for the training process. In this paper, a new approach to enhance NN training with physical knowledge using constraint optimization techniques is presented. Specific constraints for hyperelastic materials are introduced, which include energy conservation, normalization and material symmetries. We show, that the introduced enhancements lead to better learning behavior with respect to well known issues like a small number of training samples or noisy data. The NN is used as a material law within a finite element analysis and its convergence behavior is discussed with regard to the newly introduced training enhancements. The feasibility of NNs trained with physical constraints is shown for data based on real world experiments. We show, that the enhanced training outperforms state-of-the-art techniques with respect to stability and convergence behavior within FE simulations.

Automated summary

This paper presents a new approach to enhance neural network training with physical knowledge using constraint optimization techniques in computational mechanics for material behavior approximation. Specific constraints for hyperelastic materials are introduced to address issues like small training samples and noisy data. Experimental results demonstrate that training with physical constraints outperforms state-of-the-art techniques in terms of stability and convergence behavior within finite element simulations.