Physics-guided neural network architectures for modeling nonlinear behaviors: Application to shape memory alloy wires

A novel physics-guided machine learning framework is proposed for the numerical simulation of complex nonlinear behaviors and to improve the generalization capability of data-driven models under limited information conditions. It combines an a priori physics-based model with a new neural network (NN) architecture designed to compensate for its inaccuracies. A differential evolution algorithm is adopted for the parametric identification of the physics-based model. On the other hand, an original transformer-based NN, enhanced with a long short-term memory (LSTM) feature fusion layer, is employed to capture the inherent aspects of the nonlinear behavior that are overlooked by the physics-based model so as to reduce overall errors. This approach is applied to simulate the hysteretic tensile behavior of NiTiNOL shape memory alloy wires subject to different loading rates. A comprehensive experimental comparative assessment is carried out between a physics-based (phenomenological) modeling approach and several NN architectures, including the uni- and bi-directional LSTM models, a transformer model, as well as the proposed architecture merging a transformer component with either uni- or bi-directional LSTM model. These NN architectures are employed both in a fully data-driven setting and within the physics-guided framework herein conceived with the purpose of mitigating the inaccuracies arising from the selected phenomenological model and limited data. The results indicate that the proposed NN architecture connecting LSTM and transformer components achieves the best overall performance. Furthermore, the physics-guided approach consistently improves both accuracy and reliability of the predictions.