耗散系统的数据驱动离散时间深度递归神经网络建模
Data-driven discrete-time deep recurrent neural network-based modeling for dissipative systems
- Sungkyunkwan University（成均馆大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出深度离散时间耗散递归神经网络（DissipNet），通过结构权重约束和专门训练算法显式强制耗散性，利用李雅普诺夫理论保证稳定性，并在建模应用中优于朴素RNN和PINN模型。
AI中文摘要：
物理人工智能因其在开发能够更好地理解、预测和控制现实世界动态的人工智能系统中的作用而日益受到关注。实现这一目标需要人工智能模型不仅具有高预测精度，还要保留动力系统的基本物理特性。本文提出了一种深度离散时间耗散递归神经网络（DissipNet），通过结构权重约束和专门的训练算法显式地强制实现耗散性，这是与稳定性和能量耗散相关的关键特性。通过构造，所提出的网络能够学习耗散动力学，同时保持其固有的稳定性，并使用李雅普诺夫理论进行形式化分析。与将控制方程纳入训练损失但不保证保留内部解析性质（如耗散性或无源性）的物理信息神经网络（PINNs）相比，我们的方法在模型层面提供了稳定性的显式保证。我们通过几个建模应用证明了所提出方法的有效性，并将其性能与朴素递归神经网络（RNN）和基于PINN的模型进行了比较。
英文摘要：
Physical AI has gained increasing attention for its role in developing AI systems that better understand, predict, and control real-world dynamics. Achieving this requires AI models that not only achieve high prediction accuracy but also preserve fundamental physical properties of dynamical systems. In this paper, we propose a deep discrete-time dissipative recurrent neural network (DissipNet) that explicitly enforces dissipativity, a key property related to stability and energy dissipation, through structural weight constraints and a dedicated training algorithm. By construction, the proposed network is capable of learning dissipative dynamics while preserving their inherent stability, which is formally analyzed using Lyapunov theory. In contrast to Physics-Informed Neural Networks (PINNs), which incorporate governing equations into the training loss but do not guarantee preservation of internal analytical properties such as dissipativity or passivity, our approach provides explicit guarantees on stability at the model level. We demonstrate the effectiveness of the proposed method through several modeling applications, and compare its performance with a naive recurrent neural network (RNN) and a PINN-based model.
