mlsanityData to 7 Oct 2026

Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversion

arXiv 2307.07882 ↗First posted 15 Jul 2023cs.LG cs.NA cs.SYcited by 9

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Abstract (arXiv)

Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI is a gradient-free optimization method that only necessitates the evaluation of artificial neural networks in forward passes. In this study, we examine the effectiveness of EKI in training neural ordinary differential equations (neural ODEs) for system identification and control tasks. To apply EKI to optimal control problems, we formulate inverse problems that incorporate a Tikhonov-type regularization term. Our numerical results demonstrate that EKI is an efficient method for training neural ODEs in system identification and optimal control problems, with runtime and quality of solutions that are competitive with commonly used gradient-based optimizers.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 15 of its 43 references that are in the map. First posted on arXiv 15 Jul 2023.

Builds on

15 of 43 references.

References · 15

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
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  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2017Data-driven discovery of Koopman eigenfunctions for controlcited by 64
  5. 2021Optimal control of PDEs using physics-informed neural networkscited by 51
  6. 2018Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Taskscited by 36
  7. 2021Implicit energy regularization of neural ordinary-differential-equation controlcited by 29
  8. 2019Deep neural networks, generic universal interpolation, and controlled ODEscited by 28
  9. 2021Auto-differentiable Ensemble Kalman Filterscited by 28
  10. 2020Neural Ordinary Differential Equation Control of Dynamics on Graphscited by 24
  11. 2022Visualizing high-dimensional loss landscapes with Hessian directionscited by 16
  12. 2019Tikhonov Regularization Within Ensemble Kalman Inversioncited by 13
3 more
  1. 2022Near-optimal control of dynamical systems with neural ordinary differential equationscited by 9
  2. 2018Never look back - A modified EnKF method and its application to the training of neural networks without back propagationcited by 8
  3. 2020Faster Policy Learning with Continuous-Time Gradientscited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 2; 2026: 2.

9 papers.

  1. 2023Neural Dynamical Operator: Continuous Spatial-Temporal Model with Gradient-Based and Derivative-Free Optimization Methodscited by 14
  2. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  3. 2024Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Featurescited by 7
  4. 2023Online Calibration of Deep Learning Sub-Models for Hybrid Numerical Modeling Systemscited by 4
  5. 2024Control of Medical Digital Twins with Artificial Neural Networkscited by 3
  6. 2024Statistical Mechanics and Artificial Neural Networks: Principles, Models, and Applicationscited by 0
  7. 2025Control of dynamical systems with neural networkscited by 0
  8. 2026xFODE+: Explainable Type-2 Fuzzy Additive ODEs for Uncertainty Quantificationcited by 0
  9. 2026xFODE: An Explainable Fuzzy Additive ODE Framework for System Identificationcited by 0