State space neural network with nonlinear physics for mechanical system modeling

Dynamic modeling of mechanical systems is important for the monitoring, diagnostics, control, and prediction of system behaviors. Modeling dynamic systems is one of the emerging tasks in scientific machine learning. Neural networks have been used to learn surrogate models for the underlying dynamics in the form of data-driven neural ordinary differential equations (NODEs). While most dynamical mechanical systems have some degree of nonlinearity within their dynamics, neural networks have shown potential in approximating dynamic systems with nonlinearities. However, despite the universal approximation capability of neural networks, this paper argues that by adding physics-aware nonlinear functions to the neural network model, the modeling accuracy of the neural network can be increased. In this paper, the construction of the nonlinear continuous-time state-space neural network (NLCSNN) is presented. The proposed approach can be used as a data-driven method for digital twin construction for monitoring, prediction, and reliability assessment. The NLCSNN improves upon the previously established continuous-time state-space neural network by increasing sensitivity to nonlinearity. The proposed NLCSNN is trained and validated using numerical and experimental examples, with results compared against those from several existing methodologies. Validation results show that the NLCSNN model can learn complex engineering dynamics without explicit knowledge of the underlying system. The modeling performance of the proposed data-driven approach outperforms a purely physics-based model, with results comparable to hybrid models. Additionally, the NLCSNN model achieved higher accuracy than the continuous-time state-space neural network (CSNN) model.