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

Abstract: While state-space models have historically been rooted in physical principles, their utility for multi-step forecasting is often compromised by inaccuracies inherent in the underlying models. Although black-box deep learning offers a viable alternative, it typically demands extensive datasets and frequently overlooks the potential benefits of integrating existing physical knowledge. To address these limitations, we introduce the PG-RSSNN, a physics-guided recurrent state-space neural network. By embedding recurrent structures, this architecture allows for the utilization of non-saturating activation functions during multi-step prediction. This approach effectively resolves issues such as vanishing gradients and prevents numerical divergence during training—a common risk in prior architectures that relied on feedback loops for state estimation. Empirical evaluations across diverse systems, including linear state-space models with Gaussian noise, robotic arms, and cascaded water tank systems, demonstrate that PG-RSSNN achieves stable training dynamics and superior multi-step prediction accuracy. These advantages hold true even when physical models are only partially understood or when training data is scarce, outperforming both standalone physics-based models and pure black-box neural networks.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC