Physics-Guided Recurrent State-Space Neural Networks for Multi-Step Prediction

2026-06-01

AI Summary

This work addresses the limitations of traditional physics-based models, which suffer from inaccuracies that degrade multi-step prediction performance, and purely data-driven black-box neural networks, which ignore known physical laws and require extensive data. To overcome these issues, the authors propose a Physics-Guided Recurrent State-Space Neural Network (PG-RSSNN) that integrates partial physical priors into a recurrent state-space architecture and employs non-saturating activation functions to mitigate gradient vanishing and numerical divergence. The method achieves significantly improved multi-step prediction accuracy and training stability with limited training data. Experimental results demonstrate that PG-RSSNN consistently outperforms both pure physics-based models and black-box neural networks across diverse systems, including linear dynamical systems, robotic manipulators, and tank systems.

Abstract

State-space models are traditionally based on physical knowledge, but multi-step predictions from these physical models can be poor due to model inaccuracy. Black-box deep learning has shown promise as an alternative. However, these methods rely on the availability of large datasets and potentially available physical knowledge is neglected. We propose the PG-RSSNN, a physics-guided recurrent state-space neural network that incorporates recurrent structures to enable the use of non-saturating activation functions in multi-step prediction. It mitigates the vanishing gradients and eliminates the risk of numerical divergence in training seen in existing structures that feed back state estimates. Results across multiple systems with various physical model imperfections, from linear state-space models with Gaussian noise to a robotic arm and a cascaded water tank system, show that the proposed PG-RSSNN maintains stable training behavior, and improves multi-step predictions, as compared with black-box neural networks and physics-only models, even with limited training data and when physical models are only partially known.

Problem

• multi-step prediction
• state-space models
• physics-guided learning
• neural networks
• model inaccuracy

Innovation

• physics-guided
• recurrent state-space
• multi-step prediction
• non-saturating activation
• vanishing gradient mitigation