融合物理先验的递归状态空间网络，提升少数据下的多步预测稳定性与精度。
Physics-Guided Recurrent State-Space Neural Networks for Multi-Step Prediction
- 引入递归结构与非饱和激活函数，缓解梯度消失问题。
- 在有限数据和不完整物理模型下，多步预测误差低于纯神经网络与纯物理模型。
- 适用于机器人、水箱系统等复杂动态系统建模，适合缺乏大量数据的工程场景。
状态空间模型传统上基于物理知识，但因模型不准确导致多步预测性能较差。黑箱深度学习虽有潜力，却依赖大规模数据且忽视物理知识。本文提出物理引导的递归状态空间神经网络（PG-RSSNN），通过递归结构支持非饱和激活函数，缓解梯度消失并避免训练中的数值发散。在多种系统（包括带高斯噪声的线性状态空间模型、机械臂、级联水箱系统）上的实验表明，即使训练数据有限且物理模型部分已知，该方法仍保持稳定训练，并显著优于纯神经网络与纯物理模型的多步预测表现。
原文摘要 · Abstract (English)
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.
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