Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty
This work addresses the challenge of interpretability in deep learning for dynamical systems, offering a hybrid approach that could benefit researchers and practitioners in fields like control systems and physics-informed machine learning, though it appears incremental by bridging existing methods.
The paper tackles the problem of learning nonlinear dynamical systems with uncertainty by proposing a Physics-guided Deep Markov Model (PgDMM), which combines physics-based state space models with deep generative models to achieve a more structured and interpretable latent space, resulting in improved performance on simulation and experimental case studies.
In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where exact inference of latent variables is typically intractable. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space often lacks physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential for enhancing and generalizing the predictive capabilities of deep learning-based models.