# Synthesis of recurrent neural networks for dynamical system simulation

arXiv: https://arxiv.org/abs/1512.05702 · HTML: https://mlsanity.com/paper/1512.05702/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2015.

## Built on by (most cited first, 16 of 16)

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- [Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems](https://mlsanity.com/paper/2207.02542/) (2022)
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- [Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series](https://mlsanity.com/paper/2111.02922/) (2021)
- [Deep Learning of Chaotic Systems from Partially-Observed Data](https://mlsanity.com/paper/2205.08384/) (2022)
- [Generative AI and Process Systems Engineering: The Next Frontier](https://mlsanity.com/paper/2402.10977/) (2024)
- [Weak Form Generalized Hamiltonian Learning](https://mlsanity.com/paper/2104.05096/) (2021)
- [SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics](https://mlsanity.com/paper/2302.03663/) (2023)
- [On the effectiveness of neural priors in modeling dynamical systems](https://mlsanity.com/paper/2303.05728/) (2023)
- [A Differential Geometry Perspective on Orthogonal Recurrent Models](https://mlsanity.com/paper/2102.09589/) (2021)
- [Course Correcting Koopman Representations](https://mlsanity.com/paper/2310.15386/) (2023)
- [RefreshNet: Learning Multiscale Dynamics through Hierarchical Refreshing](https://mlsanity.com/paper/2401.13282/) (2024)
- [A Low-complexity Structured Neural Network to Realize States of Dynamical Systems](https://mlsanity.com/paper/2503.23697/) (2025)
- [A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems](https://mlsanity.com/paper/2607.14937/) (2026)

## Abstract (arXiv)

We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that guarantees the quality of the network approximation. We show that a feedforward neural network can be trained on the vector field representation of a given dynamical system using backpropagation, then recast, using matrix manipulations, as a recurrent network that replicates the original system's dynamics. After detailing this algorithm and its relation to earlier approaches, we present numerical examples that demonstrate its capabilities. One of the distinguishing features of our approach is that both the original dynamical systems and the recurrent networks that simulate them operate in continuous time.