Physics-Guided Recurrent State-Space Neural Networks for Multi-Step Prediction
2026-06-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors created a new type of neural network called PG-RSSNN that combines physics knowledge with deep learning to improve predictions of how systems change over time. Traditional physics-based models can be inaccurate, and pure deep learning models need lots of data and ignore physics. Their PG-RSSNN uses special structures to avoid common training problems and works well even when only limited data and imperfect physics models are available. They tested it on different systems like robotic arms and water tanks, showing it predicts better than just physics or pure learning approaches.
state-space modelsrecurrent neural networksvanishing gradientsmulti-step predictionphysics-guided learningblack-box modelsnumerical divergenceGaussian noiserobotic systemswater tank system
Authors
Ruiyuan Li, Ajay Seth, Manon Kok
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.