TorchDyn: A Neural Differential Equations Library
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Abstract (arXiv)
Continuous-depth learning has recently emerged as a novel perspective on deep learning, improving performance in tasks related to dynamical systems and density estimation. Core to these approaches is the neural differential equation, whose forward passes are the solutions of an initial value problem parametrized by a neural network. Unlocking the full potential of continuous-depth models requires a different set of software tools, due to peculiar differences compared to standard discrete neural networks, e.g inference must be carried out via numerical solvers. We introduce TorchDyn, a PyTorch library dedicated to continuous-depth learning, designed to elevate neural differential equations to be as accessible as regular plug-and-play deep learning primitives. This objective is achieved by identifying and subdividing different variants into common essential components, which can be combined and freely repurposed to obtain complex compositional architectures. TorchDyn further offers step-by-step tutorials and benchmarks designed to guide researchers and contributors.
Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Sep 2020.
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Citing papers per year: 2021: 6; 2022: 5; 2023: 3; 2024: 1; 2025: 1.
16 papers.
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- 2023Deep networks for system identification: a Surveycited by 35
- 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
- 2023TorchDEQ: A Library for Deep Equilibrium Modelscited by 21
- 2021Differentiable Multiple Shooting Layerscited by 20
- 2022Neural Ordinary Differential Equations for Nonlinear System Identificationcited by 14
- 2021Sparse Flows: Pruning Continuous-depth Modelscited by 13
- 2021Accelerating Neural ODEs Using Model Order Reductioncited by 9
- 2021Continuous-Depth Neural Models for Dynamic Graph Predictioncited by 7
- 2022Self-Similarity Priors: Neural Collages as Differentiable Fractal Representationscited by 6
- 2021Optimal Energy Shaping via Neural Approximatorscited by 4
- 2022Neural Solvers for Fast and Accurate Numerical Optimal Controlcited by 4
- 2022A Neural Ordinary Differential Equation Model for Visualizing Deep Neural Network Behaviors in Multi-Parametric MRI based Glioma Segmentationcited by 2
4 more
- 2024Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approachcited by 2
- 2025High-order expansion of Neural Ordinary Differential Equations flowscited by 1
- 2021Freudian and Newtonian Recurrent Cell for Sequential Recommendationcited by 0
- 2023On the Benefits of Biophysical Synapsescited by 0
- 2025High-order expansion of Neural Ordinary Differential Equations flows2 Apr 2025
- 2024Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach15 Nov 2024
- 2023TorchDEQ: A Library for Deep Equilibrium Models28 Oct 2023
- 2023On the Benefits of Biophysical Synapses8 Mar 2023
- 2023Deep networks for system identification: a Survey30 Jan 2023
- 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing14 Nov 2022
- 2022Self-Similarity Priors: Neural Collages as Differentiable Fractal Representations15 Apr 2022
- 2022Neural Solvers for Fast and Accurate Numerical Optimal Control13 Mar 2022
- 2022A Neural Ordinary Differential Equation Model for Visualizing Deep Neural Network Behaviors in Multi-Parametric MRI based Glioma Segmentation1 Mar 2022
- 2022Neural Ordinary Differential Equations for Nonlinear System Identification28 Feb 2022
- 2021Sparse Flows: Pruning Continuous-depth Models24 Jun 2021
- 2021Continuous-Depth Neural Models for Dynamic Graph Prediction22 Jun 2021
4 more
- 2021Differentiable Multiple Shooting Layers7 Jun 2021
- 2021Accelerating Neural ODEs Using Model Order Reduction28 May 2021
- 2021Freudian and Newtonian Recurrent Cell for Sequential Recommendation11 Feb 2021
- 2021Optimal Energy Shaping via Neural Approximators14 Jan 2021
- 2023Deep networks for system identification: a Surveycited by 35
- 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
- 2023TorchDEQ: A Library for Deep Equilibrium Modelscited by 21
- 2021Differentiable Multiple Shooting Layerscited by 20
- 2022Neural Ordinary Differential Equations for Nonlinear System Identificationcited by 14
- 2021Sparse Flows: Pruning Continuous-depth Modelscited by 13
- 2021Accelerating Neural ODEs Using Model Order Reductioncited by 9
- 2021Continuous-Depth Neural Models for Dynamic Graph Predictioncited by 7
- 2022Self-Similarity Priors: Neural Collages as Differentiable Fractal Representationscited by 6
- 2021Optimal Energy Shaping via Neural Approximatorscited by 4
- 2022Neural Solvers for Fast and Accurate Numerical Optimal Controlcited by 4
- 2022A Neural Ordinary Differential Equation Model for Visualizing Deep Neural Network Behaviors in Multi-Parametric MRI based Glioma Segmentationcited by 2
12 most cited of 16 All 16 (JSON)
- 2025High-order expansion of Neural Ordinary Differential Equations flows2 Apr 2025
- 2024Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach15 Nov 2024
- 2023TorchDEQ: A Library for Deep Equilibrium Models28 Oct 2023
- 2023On the Benefits of Biophysical Synapses8 Mar 2023
- 2023Deep networks for system identification: a Survey30 Jan 2023
- 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing14 Nov 2022
- 2022Self-Similarity Priors: Neural Collages as Differentiable Fractal Representations15 Apr 2022
- 2022Neural Solvers for Fast and Accurate Numerical Optimal Control13 Mar 2022
- 2022A Neural Ordinary Differential Equation Model for Visualizing Deep Neural Network Behaviors in Multi-Parametric MRI based Glioma Segmentation1 Mar 2022
- 2022Neural Ordinary Differential Equations for Nonlinear System Identification28 Feb 2022
- 2021Sparse Flows: Pruning Continuous-depth Models24 Jun 2021
- 2021Continuous-Depth Neural Models for Dynamic Graph Prediction22 Jun 2021
12 newest of 16 All 16 (JSON)