mlsanityData to 7 Oct 2026

Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems

arXiv 2010.14685 ↗First posted 28 Oct 2020physics.comp-ph cs.AIcited by 45

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Abstract (arXiv)

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ordinary differential equations, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder-decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs with important benchmark problems from computational physics.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Oct 2020.

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Citing papers per year: 2021: 4; 2022: 3; 2023: 6; 2024: 11; 2025: 14; 2026: 7.

45 papers.

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  1. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  2. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  3. 2024On latent dynamics learning in nonlinear reduced order modelingcited by 14
  4. 2024When are dynamical systems learned from time series data statistically accurate?cited by 14
  5. 2021Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equationscited by 13
  6. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  7. 2024CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equationscited by 12
  8. 2022Operator inference with roll outs for learning reduced models from scarce and low-quality datacited by 11
  9. 2023Metalearning generalizable dynamics from trajectoriescited by 9
  10. 2024Neural Context Flows for Meta-Learning of Dynamical Systemscited by 9
  11. 2024Efficient, Accurate and Stable Gradients for Neural ODEscited by 9
  12. 2024Parametric model reduction of mean-field and stochastic systems via higher-order action matchingcited by 8
33 more
  1. 2025Thermodynamically Consistent Latent Dynamics Identification for Parametric Systemscited by 8
  2. 2023Reduced-order modeling for parameterized PDEs via implicit neural representationscited by 7
  3. 2025Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamicscited by 4
  4. 2025Neural Ordinary Differential Equations for Learning and Extrapolating System Dynamics Across Bifurcationscited by 4
  5. 2023Do We Need an Encoder-Decoder to Model Dynamical Systems on Networks?cited by 3
  6. 2024Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditionscited by 3
  7. 2024Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximationscited by 3
  8. 2025Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solverscited by 2
  9. 2025Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivativescited by 2
  10. 2021Incorporating NODE with Pre-trained Neural Differential Operator for Learning Dynamicscited by 1
  11. 2022Mining Causality from Continuous-time Dynamics Models: An Application to Tsunami Forecastingcited by 1
  12. 20243D-PDR Orion dataset and NeuralPDR: Neural Differential Equations for Photodissociation Regionscited by 1
  13. 2025Invariant Measures for Data-Driven Dynamical System Identification: Analysis and Applicationcited by 1
  14. 2025Understanding the role of autoencoders for stiff dynamical systems using information theorycited by 1
  15. 2025NeuralPDR: Neural Differential Equations as surrogate models for Photodissociation Regionscited by 1
  16. 2025Learning solutions of parameterized stiff ODEs using Gaussian processescited by 1
  17. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  18. 2026A deep learning framework for jointly solving transient Fokker-Planck equations with arbitrary parameters and initial distributionscited by 1
  19. 2026Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEscited by 1
  20. 2022Parameter-varying neural ordinary differential equations with partition-of-unity networkscited by 0
  21. 2023Physics-based parameterized neural ordinary differential equations: prediction of laser ignition in a rocket combustorcited by 0
  22. 2023Efficient Learning of PDEs via Taylor Expansion and Sparse Decomposition into Value and Fourier Domainscited by 0
  23. 2023Differentiable DG with Neural Operator Source Term Correctioncited by 0
  24. 2024Modeling chaotic Lorenz ODE System using Scientific Machine Learningcited by 0
  25. 2024A comparative study of NeuralODE and Universal ODE approaches to solving Chandrasekhar White Dwarf equationcited by 0
  26. 2025LiLaN: A Linear Latent Network as the Solution Operator for Real-Time Solutions to Stiff Nonlinear Ordinary Differential Equationscited by 0
  27. 2025Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurementscited by 0
  28. 2025Revealing Low-Dimensional Structure in 2D Richtmyer-Meshkov Instabilities via Parametric Reduced-Order Modelingcited by 0
  29. 2025Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equationscited by 0
  30. 2026Data-driven stochastic reduced-order modeling of parametrized dynamical systemscited by 0
  31. 2026Generative prediction of laser-induced rocket ignition with dynamic latent space representationscited by 0
  32. 2026Frequency-Domain Neural ODEs for Modeling Non-Linear Dynamical Systemscited by 0
  33. 2026Continuous-Time Machine Learning: A Unified Mathematical Perspectivecited by 0