mlsanityData to 14 Oct 2026

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data

arXiv 1908.03190 ↗First posted 8 Aug 2019cs.LG stat.MLcited by 42

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Abstract (arXiv)

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing system which respects the intrinsic differential structure. The unknown governing model is parameterized by using both (shallow) multilayer perceptrons and nonlinear differential terms, in order to incorporate relevant correlations between spatio-temporal samples. We demonstrate the approach on several examples where the data is sampled from various dynamical systems and give a comparison to recurrent networks and other data-discovery methods. In addition, we show that for MNIST and Fashion MNIST, our approach lowers the parameter cost as compared to other deep neural networks.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). First posted on arXiv 8 Aug 2019.

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Citing papers per year: 2021: 15; 2022: 8; 2023: 6; 2024: 7; 2025: 4; 2026: 2.

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  1. 2025A Survey of Sim-to-Real Methods in RL: Progress, Prospects and Challenges with Foundation Modelscited by 38
  2. 2024PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamicscited by 34
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  4. 2021Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Spacecited by 25
  5. 2023Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarkscited by 18
  6. 2021Beyond Predictions in Neural ODEs: Identification and Interventionscited by 15
  7. 2021The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimationcited by 14
  8. 2024LeMON: Learning to Learn Multi-Operator Networkscited by 14
  9. 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
  10. 2023Deep-OSG: Deep Learning of Operators in Semigroupcited by 11
  11. 2022Deep Learning of Chaotic Systems from Partially-Observed Datacited by 9
  12. 2025DUE: A Deep Learning Framework and Library for Modeling Unknown Equationscited by 8
30 more
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  4. 2021Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamicscited by 5
  5. 2022Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learningcited by 5
  6. 2024AsCAN: Asymmetric Convolution-Attention Networks for Efficient Recognition and Generationcited by 5
  7. 2022Neural Piecewise-Constant Delay Differential Equationscited by 4
  8. 2022Modeling unknown dynamical systems with hidden parameterscited by 4
  9. 2023Learning PDE Solution Operator for Continuous Modeling of Time-Seriescited by 3
  10. 2021Neuro-Reachability of Networked Microgridscited by 2
  11. 2021A Swarm Variant for the Schr"odinger Solvercited by 2
  12. 2021Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEscited by 2
  13. 2021Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Datacited by 2
  14. 2023Graph Neural Stochastic Differential Equationscited by 2
  15. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  16. 2026Autoregression-Free Neural Operators for Time-Dependent PDEscited by 2
  17. 2021Signature-Graph Networkscited by 1
  18. 2021Characteristic Neural Ordinary Differential Equationscited by 1
  19. 2022Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrencecited by 1
  20. 2022Symplectically Integrated Symbolic Regression of Hamiltonian Dynamical Systemscited by 1
  21. 2024DDE-Find: Learning Delay Differential Equations from Noisy, Limited Datacited by 1
  22. 2026MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Datacited by 1
  23. 2021Accuracy and Architecture Studies of Residual Neural Network solving Ordinary Differential Equationscited by 0
  24. 2021Modelling Neuronal Behaviour with Time Series Regression: Recurrent Neural Networks on C. Elegans Datacited by 0
  25. 2022E2V-SDE: From Asynchronous Events to Fast and Continuous Video Reconstruction via Neural Stochastic Differential Equationscited by 0
  26. 2023Neural Delay Differential Equations: System Reconstruction and Image Classificationcited by 0
  27. 2023Physics informed Neural Networks applied to the description of wave-particle resonance in kinetic simulations of fusion plasmascited by 0
  28. 2024Recent Trends in Modelling the Continuous Time Series using Deep Learning: A Surveycited by 0
  29. 2024Deep Trees for (Un)structured Data: Tractability, Performance, and Interpretabilitycited by 0
  30. 2025Multi-Task Neural Architecture Search Using Architecture Embedding and Transfer Rankcited by 0