# Neural Integration of Continuous Dynamics

arXiv: https://arxiv.org/abs/1911.10309 · HTML: https://mlsanity.com/paper/1911.10309/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2019.

## Built on by (most cited first, 3 of 3)

- [Learn Like The Pro: Norms from Theory to Size Neural Computation](https://mlsanity.com/paper/2106.11409/) (2021)
- [Multirotor Ensemble Model Predictive Control I: Simulation Experiments](https://mlsanity.com/paper/2305.12625/) (2023)
- [The Physics Is the Network: Fast, Training-Free Neural Emulation](https://mlsanity.com/paper/2610.20525/) (2026)

## Abstract (arXiv)

Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we present a compact neural circuit for two common numerical integrators: the explicit fixed-step Runge-Kutta method of any order and the semi-implicit/predictor-corrector Adams-Bashforth-Moulton method. Modeled as constant-sized recurrent networks embedding a continuous neural differential equation, they achieve fully neural temporal output. Using the polynomial class of dynamical systems, we demonstrate the equivalence of neural and numerical integration.