# Dissipative Deep Neural Dynamical Systems

arXiv: https://arxiv.org/abs/2011.13492 · HTML: https://mlsanity.com/paper/2011.13492/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2020.

## Built on by (most cited first, 12 of 12)

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- [Learning Dissipative Neural Dynamical Systems](https://mlsanity.com/paper/2309.16032/) (2023)
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- [Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles](https://mlsanity.com/paper/2208.07333/) (2022)
- [DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecasting](https://mlsanity.com/paper/2508.02616/) (2025)
- [Constraint Breeds Generalization: Temporal Dynamics as an Inductive Bias](https://mlsanity.com/paper/2512.23916/) (2025)
- [Stability Enhanced Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2604.09331/) (2026)
- [Data-driven discrete-time deep recurrent neural network-based modeling for dissipative systems](https://mlsanity.com/paper/2609.27186/) (2026)

## Abstract (arXiv)

In this paper, we provide sufficient conditions for dissipativity and local asymptotic stability of discrete-time dynamical systems parametrized by deep neural networks. We leverage the representation of neural networks as pointwise affine maps, thus exposing their local linear operators and making them accessible to classical system analytic and design methods. This allows us to "crack open the black box" of the neural dynamical system's behavior by evaluating their dissipativity, and estimating their stationary points and state-space partitioning. We relate the norms of these local linear operators to the energy stored in the dissipative system with supply rates represented by their aggregate bias terms. Empirically, we analyze the variance in dynamical behavior and eigenvalue spectra of these local linear operators with varying weight factorizations, activation functions, bias terms, and depths.