A Physics-Guided Deep Learning Approach to Modeling Nonlinear Dynamics: A Case Study of a Bouc-Wen System

Abstract

In this paper, we study the feasibility of applying the recently proposed Physicsguided Deep Markov Model (PgDMM) [1] for the modeling of hysteretic systems. PgDMM forms a hybrid probabilistic physics-guided framework, bridging physicsbased state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. Previously, the framework has been tested on nonlinear elastic systems while in this work, we further test the framework on hysteretic systems described by Bouc-Wen type hysteresis. A physics-based model is used, which partially models the systems dynamics, which is implemented by a learning-based term parameterized by a neural network. Our results indicate that the physics-based model essentially enforces a more structured and physically interpretable latent space, which is essential for generalization and prediction capabilities.