# dynoNet: a neural network architecture for learning dynamical systems

arXiv: https://arxiv.org/abs/2006.02250 · HTML: https://mlsanity.com/paper/2006.02250/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 29 of 29)

- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [From system models to class models: An in-context learning paradigm](https://mlsanity.com/paper/2308.13380/) (2023)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Baseline Results for Selected Nonlinear System Identification Benchmarks](https://mlsanity.com/paper/2405.10779/) (2024)
- [On the adaptation of in-context learners for system identification](https://mlsanity.com/paper/2312.04083/) (2023)
- [Differentiable All-pole Filters for Time-varying Audio Systems](https://mlsanity.com/paper/2404.07970/) (2024)
- [Enhanced Transformer architecture for in-context learning of dynamical systems](https://mlsanity.com/paper/2410.03291/) (2024)
- [Continuous-time identification of dynamic state-space models by deep subspace encoding](https://mlsanity.com/paper/2204.09405/) (2022)
- [Learning neural state-space models: do we need a state estimator?](https://mlsanity.com/paper/2206.12928/) (2022)
- [Model order reduction of deep structured state-space models: A system-theoretic approach](https://mlsanity.com/paper/2403.14833/) (2024)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Synthetic data generation for system identification: leveraging knowledge transfer from similar systems](https://mlsanity.com/paper/2403.05164/) (2024)
- [Structured state-space models are deep Wiener models](https://mlsanity.com/paper/2312.06211/) (2023)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [dynoGP: Deep Gaussian Processes for dynamic system identification](https://mlsanity.com/paper/2502.05620/) (2025)
- [Neural Entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws](https://mlsanity.com/paper/2507.01795/) (2025)
- [Efficient identification of linear, parameter-varying, and nonlinear systems with noise models](https://mlsanity.com/paper/2504.11982/) (2025)
- [Deep learning with transfer functions: new applications in system identification](https://mlsanity.com/paper/2104.09839/) (2021)
- [Bayesian Inference and Learning in Nonlinear Dynamical Systems: A Framework for Incorporating Explicit and Implicit Prior Knowledge](https://mlsanity.com/paper/2508.15345/) (2025)
- [Tuning the burn-in phase in training recurrent neural networks improves their performance](https://mlsanity.com/paper/2602.10911/) (2026)
- [Controller Design for Structured State-space Models via Contraction Theory](https://mlsanity.com/paper/2604.07069/) (2026)
- [Orthogonal Transforms in Neural Networks Amount to Effective Regularization](https://mlsanity.com/paper/2305.06344/) (2023)
- [Exploiting the capacity of deep networks only at training stage for nonlinear black-box system identification](https://mlsanity.com/paper/2312.15969/) (2023)
- [Entropy stable conservative flux form neural networks](https://mlsanity.com/paper/2411.01746/) (2024)
- [Diffusion Sequence Models for Generative In-Context Meta-Learning of Robot Dynamics](https://mlsanity.com/paper/2604.13366/) (2026)
- [Tensor Network Kernel Machines: A JAX Framework for Machine Learning and Nonlinear System Identification](https://mlsanity.com/paper/2608.07043/) (2026)
- [In-Context Learning for System Identification: Probabilistic Formulation, Long-Sequence Handling, and Benchmark Validation](https://mlsanity.com/paper/2610.13411/) (2026)

## Abstract (arXiv)

This paper introduces a network architecture, called dynoNet, utilizing linear dynamical operators as elementary building blocks. Owing to the dynamical nature of these blocks, dynoNet networks are tailored for sequence modeling and system identification purposes. The back-propagation behavior of the linear dynamical operator with respect to both its parameters and its input sequence is defined. This enables end-to-end training of structured networks containing linear dynamical operators and other differentiable units, exploiting existing deep learning software. Examples show the effectiveness of the proposed approach on well-known system identification benchmarks. Examples show the effectiveness of the proposed approach against well-known system identification benchmarks.