State Space Neural Network with Nonlinear Physics for Mechanical System Modeling

Published

February 19, 2025

Author(s)

Reese Eischens, Tao Li, Gregory Vogl, Yi Cai, Yongzhi Qu

Abstract

Dynamic modeling of mechanical systems is important for the monitoring, diagnostics, control, and prediction of system behaviors. Modeling dynamic system 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 (NODE). Most dynamical mechanical systems have some degree of nonlinearity within their dynamics. Neural networks have shown the potential to approximate 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 neural network will have an increased modeling accuracy. In this paper, the construction of the nonlinear continuous time state space neural network (NLCSNN) is presented. The NLCSNN improves upon the previously established continuous time state space neural network by increasing the susceptibility towards nonlinearity. The proposed NLCSNN is trained and validated using numerical and experimental examples with results compared against those from several existing methodologies. The validation results show that the NLCSNN model can learn complex engineering dynamics without explicitly known knowledge of the underlying system. The modeling performance of the proposed data-driven approach outperforms a pure physics-based model with results that are comparable to hybrid models. Also, the NLCSNN model achieved higher accuracy than the continuous time state space neural network (CSNN) model.

Citation

Reliability Engineering & System Safety

Pub Type

Journals

Download Paper

https://doi.org/10.1016/j.ress.2025.110946

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Citation

Eischens, R. , Li, T. , Vogl, G. , Cai, Y. and Qu, Y. (2025), State Space Neural Network with Nonlinear Physics for Mechanical System Modeling, Reliability Engineering & System Safety, [online], https://doi.org/10.1016/j.ress.2025.110946, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=958112 (Accessed October 8, 2025)