mlsanityData to 7 Oct 2026

torchode: A Parallel ODE Solver for PyTorch

arXiv 2210.12375 ↗First posted 22 Oct 2022cs.LG cs.NA math.NAcited by 10

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Abstract (arXiv)

We introduce an ODE solver for the PyTorch ecosystem that can solve multiple ODEs in parallel independently from each other while achieving significant performance gains. Our implementation tracks each ODE's progress separately and is carefully optimized for GPUs and compatibility with PyTorch's JIT compiler. Its design lets researchers easily augment any aspect of the solver and collect and analyze internal solver statistics. In our experiments, our implementation is up to 4.3 times faster per step than other ODE solvers and it is robust against within-batch interactions that lead other solvers to take up to 4 times as many steps. Code available at https://github.com/martenlienen/torchode

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 18 of its 29 references that are in the map. First posted on arXiv 22 Oct 2022.

Builds on

18 of 29 references.

References · 18

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  4. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  5. 2019Augmented Neural ODEscited by 396
  6. 2022On Neural Differential Equationscited by 264
  7. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  8. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  9. 2019Graph Neural Ordinary Differential Equationscited by 153
  10. 2020Dissecting Neural ODEscited by 150
  11. 2019ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEscited by 83
  12. 2020STEER: Simple Temporal Regularization For Neural ODEscited by 58
6 more
  1. 2021Neural ODE Processescited by 57
  2. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  3. 2019DiffEqFlux.jl - A Julia Library for Neural Differential Equationscited by 33
  4. 2022Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networkscited by 33
  5. 2021Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristicscited by 26
  6. 2020ResNet After All? Neural ODEs and Their Numerical Solutioncited by 20

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 5; 2026: 3.

10 papers.

  1. 2025ODE-GS: Latent ODEs for Dynamic Scene Extrapolation with 3D Gaussian Splattingcited by 11
  2. 2025Identifiability Challenges in Sparse Linear Ordinary Differential Equationscited by 7
  3. 2024DeNOTS: Stable Deep Neural ODEs for Time Seriescited by 5
  4. 2025Scientific Machine Learning of Flow Resistance Using Universal Shallow Water Equations with Differentiable Programmingcited by 3
  5. 2023Benchmarking Continuous Time Models for Predicting Multiple Sclerosis Progressioncited by 2
  6. 2025Generative Video Bi-flowcited by 2
  7. 2026A Generalizable Physics-guided Causal Model for Trajectory Prediction in Autonomous Drivingcited by 1
  8. 2026SELDON: Supernova Explosions Learned by Deep ODE Networkscited by 1
  9. 2025evoxels: A differentiable physics framework for voxel-based microstructure simulationscited by 0
  10. 2026GRADSOLVE: fast exact gradients for ODE ensembles on GPUscited by 0