Data-driven discrete-time deep recurrent neural network-based modeling for dissipative systems

Abstract: 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.