# Control of dynamical systems with neural networks

arXiv: https://arxiv.org/abs/2510.12810 · HTML: https://mlsanity.com/paper/2510.12810/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 135 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 30 of 43)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Improving Sample Efficiency in Model-Free Reinforcement Learning from Images](https://mlsanity.com/paper/1910.01741/) (2019)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Continuously Differentiable Exponential Linear Units](https://mlsanity.com/paper/1704.07483/) (2017)
- [Deep Reinforcement Learning for Sepsis Treatment](https://mlsanity.com/paper/1711.09602/) (2017)
- [Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework](https://mlsanity.com/paper/1912.12970/) (2019)
- [Optimal control of PDEs using physics-informed neural networks](https://mlsanity.com/paper/2111.09880/) (2021)
- [LyaNet: A Lyapunov Framework for Training Neural ODEs](https://mlsanity.com/paper/2202.02526/) (2022)
- [Implicit energy regularization of neural ordinary-differential-equation control](https://mlsanity.com/paper/2103.06525/) (2021)
- [Automatic Differentiation of Programs with Discrete Randomness](https://mlsanity.com/paper/2210.08572/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [Neural Ordinary Differential Equation Control of Dynamics on Graphs](https://mlsanity.com/paper/2006.09773/) (2020)
- [Interpretable Polynomial Neural Ordinary Differential Equations](https://mlsanity.com/paper/2208.05072/) (2022)
- [A Survey on Physics Informed Reinforcement Learning: Review and Open Problems](https://mlsanity.com/paper/2309.01909/) (2023)
- [Differentiable Agent-based Epidemiology](https://mlsanity.com/paper/2207.09714/) (2022)
- [Physics-Informed Model-Based Reinforcement Learning](https://mlsanity.com/paper/2212.02179/) (2022)
- [Input Convex Neural Networks for Building MPC](https://mlsanity.com/paper/2011.13227/) (2020)
- [Why ReLU Units Sometimes Die: Analysis of Single-Unit Error Backpropagation in Neural Networks](https://mlsanity.com/paper/1812.05981/) (2018)
- [Uncertainty Quantification of Surrogate Models using Conformal Prediction](https://mlsanity.com/paper/2408.09881/) (2024)
- [Near-optimal control of dynamical systems with neural ordinary differential equations](https://mlsanity.com/paper/2206.11120/) (2022)

## Abstract (arXiv)

Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation have made applying these methods to control problems increasingly practical. In this paper, we examine the use of neural networks and modern machine-learning libraries to parameterize control inputs across discrete-time and continuous-time systems, as well as deterministic and stochastic dynamics. We highlight applications in multiple domains, including biology, engineering, physics, and medicine. For continuous-time dynamical systems, neural ordinary differential equations (neural ODEs) offer a useful approach to parameterizing control inputs. For discrete-time systems, we show how custom control-input parameterizations can be implemented and optimized using automatic-differentiation methods. Overall, the methods presented provide practical solutions for control tasks that are computationally demanding or analytically intractable, making them valuable for complex real-world applications.