# Implicit energy regularization of neural ordinary-differential-equation control arXiv: https://arxiv.org/abs/2103.06525 ยท HTML: https://mlsanity.com/paper/2103.06525/ ## Key facts - Cited by 29 papers in the map (data through 14 Oct 2026). - Builds on 13 of its 64 references that are in the map. - First posted on arXiv 11 Mar 2021. ## Builds on (most cited first, 13 of 13) - [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015) - [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015) - [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) - [Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework](https://mlsanity.com/paper/1912.12970/) (2019) - [Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics](https://mlsanity.com/paper/2005.14617/) (2020) - [Neural Ordinary Differential Equation Control of Dynamics on Graphs](https://mlsanity.com/paper/2006.09773/) (2020) - [Controllability Metrics, Limitations and Algorithms for Complex Networks](https://mlsanity.com/paper/1308.1201/) (2013) - [Realistic Control of Network Dynamics](https://mlsanity.com/paper/1307.0015/) (2013) - [Minimal Controllability Problems](https://mlsanity.com/paper/1304.3071/) (2013) - [A stochastic approach to the synchronization of coupled oscillators](https://mlsanity.com/paper/2002.04472/) (2020) - [Controllability transition and nonlocality in network control](https://mlsanity.com/paper/1305.5848/) (2013) - [Learning Control of Quantum Systems](https://mlsanity.com/paper/2101.07461/) (2021) ## Built on by (most cited first, 29 of 29) - [Visualizing high-dimensional loss landscapes with Hessian directions](https://mlsanity.com/paper/2208.13219/) (2022) - [Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems](https://mlsanity.com/paper/2202.02710/) (2022) - [Near-optimal control of dynamical systems with neural ordinary differential equations](https://mlsanity.com/paper/2206.11120/) (2022) - [On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solver](https://mlsanity.com/paper/2208.03680/) (2022) - [Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversion](https://mlsanity.com/paper/2307.07882/) (2023) - [A Pontryagin Perspective on Reinforcement Learning](https://mlsanity.com/paper/2405.18100/) (2024) - [Control of Dual-Sourcing Inventory Systems using Recurrent Neural Networks](https://mlsanity.com/paper/2201.06126/) (2022) - [Online Control-Informed Learning](https://mlsanity.com/paper/2410.03924/) (2024) - [Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression](https://mlsanity.com/paper/2411.06833/) (2024) - [Offline Supervised Learning V.S. 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In this Letter we present a versatile neural ordinary-differential-equation control (NODEC) framework with implicit energy regularization and use it to obtain neural-network-generated control signals that can steer dynamical systems towards a desired target state within a predefined amount of time. We demonstrate the ability of NODEC to learn control signals that closely resemble those found by corresponding optimal control frameworks in terms of control energy and deviation from the desired target state. Our results suggest that NODEC is capable to solve a wide range of control and optimization problems, including those that are analytically intractable.