mlsanityData to 14 Oct 2026

Differential Equations for Continuous-Time Deep Learning

arXiv 2401.03965 ↗First posted 8 Jan 2024cs.LG math.DScited by 7

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Abstract (arXiv)

This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and partial differential equations and their analysis who are curious to see their role in machine learning. Using three examples from machine learning and applied mathematics, we will see how neural ODEs can provide new insights into deep learning and a foundation for more efficient algorithms.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 21 of its 29 references that are in the map. First posted on arXiv 8 Jan 2024.

Builds on

21 of 29 references.

References · 21

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,150
  3. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 506
  4. 2019Augmented Neural ODEscited by 397
  5. 2017Stable Architectures for Deep Neural Networkscited by 341
  6. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  7. 2019Universal Approximation with Deep Narrow Networkscited by 200
  8. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  9. 2020Dissecting Neural ODEscited by 153
  10. 2020OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transportcited by 143
  11. 2021An Introduction to Deep Generative Modelingcited by 104
  12. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 97
9 more
  1. 2019ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEscited by 84
  2. 2017Maximum Principle Based Algorithms for Deep Learningcited by 78
  3. 2019Deep Learning via Dynamical Systems: An Approximation Perspectivecited by 78
  4. 2020Discretize-Optimize vs. Optimize-Discretize for Time-Series Regression and Continuous Normalizing Flowscited by 37
  5. 2019Deep learning as optimal control problems: models and numerical methodscited by 34
  6. 2019Potential Flow Generator with L2 Optimal Transport Regularity for Generative Modelscited by 31
  7. 2023A mean-field games laboratory for generative modelingcited by 28
  8. 2022Do Residual Neural Networks discretize Neural Ordinary Differential Equations?cited by 27
  9. 2020Fractional Deep Neural Network via Constrained Optimizationcited by 13

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 3; 2026: 1.

7 papers.

  1. 2024Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methodscited by 11
  2. 2024Interplay between depth and width for interpolation in neural ODEscited by 9
  3. 2025The Seismic Wavefield Common Task Frameworkcited by 6
  4. 2024Training Stiff Neural Ordinary Differential Equations with Explicit Exponential Integration Methodscited by 5
  5. 2026CTF4Nuclear: Common Task Framework for Nuclear Fission and Fusion Modelscited by 5
  6. 2025The Vanishing Gradient Problem for Stiff Neural Differential Equationscited by 3
  7. 2025Weight-Parameterization in Continuous Time Deep Neural Networks for Surrogate Modelingcited by 0