mlsanityData to 7 Oct 2026

Neural Jump Stochastic Differential Equations

arXiv 1905.10403 ↗First posted 24 May 2019cs.LG stat.MLcited by 147

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Abstract (arXiv)

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they are affected by jumps. To this end, we introduce Neural Jump Stochastic Differential Equations that provide a data-driven approach to learn continuous and discrete dynamic behavior, i.e., hybrid systems that both flow and jump. Our approach extends the framework of Neural Ordinary Differential Equations with a stochastic process term that models discrete events. We then model temporal point processes with a piecewise-continuous latent trajectory, where the discontinuities are caused by stochastic events whose conditional intensity depends on the latent state. We demonstrate the predictive capabilities of our model on a range of synthetic and real-world marked point process datasets, including classical point processes (such as Hawkes processes), awards on Stack Overflow, medical records, and earthquake monitoring.

Key facts. Cited by 147 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 May 2019.

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Citing papers per year: 2021: 29; 2022: 26; 2023: 25; 2024: 27; 2025: 21; 2026: 19.

147 papers.

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  1. 2022Liquid Structural State-Space Modelscited by 134
  2. 2021Neural Temporal Point Processes: A Reviewcited by 113
  3. 2021Modeling Irregular Time Series with Continuous Recurrent Unitscited by 101
  4. 2021Neural Flows: Efficient Alternative to Neural ODEscited by 99
  5. 2021Efficient and Accurate Gradients for Neural SDEscited by 68
  6. 2024ContiFormer: Continuous-Time Transformer for Irregular Time Series Modelingcited by 61
  7. 2021Neural ODE Processescited by 57
  8. 2023Spatio-temporal Diffusion Point Processescited by 52
  9. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  10. 2022GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networkscited by 43
  11. 2021MALI: A memory efficient and reverse accurate integrator for Neural ODEscited by 42
  12. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
38 more
  1. 2021Neural Point Process for Learning Spatiotemporal Event Dynamicscited by 42
  2. 2021Continuous-Time Model-Based Reinforcement Learningcited by 39
  3. 2023Non-adversarial training of Neural SDEs with signature kernel scorescited by 36
  4. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 35
  5. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
  6. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  7. 2022Learning continuous models for continuous physicscited by 28
  8. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  9. 2022Neural Laplace: Learning diverse classes of differential equations in the Laplace domaincited by 24
  10. 2021Causal Navigation by Continuous-time Neural Networkscited by 23
  11. 2022Bellman Meets Hawkes: Model-Based Reinforcement Learning via Temporal Point Processescited by 23
  12. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  13. 2023Add and Thin: Diffusion for Temporal Point Processescited by 22
  14. 2022On Numerical Integration in Neural Ordinary Differential Equationscited by 21
  15. 2024Trajectory Flow Matching with Applications to Clinical Time Series Modelingcited by 21
  16. 2021Differentiable Multiple Shooting Layerscited by 20
  17. 2023Learning to Simulate Daily Activities via Modeling Dynamic Human Needscited by 20
  18. 2024Functional Bilevel Optimization for Machine Learningcited by 20
  19. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  20. 2021Learning the temporal evolution of multivariate densities via normalizing flowscited by 18
  21. 2022Learning Stochastic Dynamics with Statistics-Informed Neural Networkcited by 16
  22. 2022Markovian Gaussian Process Variational Autoencoderscited by 16
  23. 2023Latent SDEs on Homogeneous Spacescited by 16
  24. 2022Statistical Deep Learning for Spatial and Spatio-Temporal Datacited by 15
  25. 2021Neural network stochastic differential equation models with applications to financial data forecastingcited by 14
  26. 2022Neural Ordinary Differential Equations for Nonlinear System Identificationcited by 14
  27. 2023Energy-Dissipative Evolutionary Deep Operator Neural Networkscited by 14
  28. 2024Continuous Temporal Domain Generalizationcited by 14
  29. 2022MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problemscited by 13
  30. 2023Neural Markov Jump Processescited by 11
  31. 2024Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methodscited by 11
  32. 2021An Empirical Study: Extensive Deep Temporal Point Processcited by 10
  33. 2022Stop&Hop: Early Classification of Irregular Time Seriescited by 10
  34. 2022Robotic Table Wiping via Reinforcement Learning and Whole-body Trajectory Optimizationcited by 10
  35. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  36. 2022Fractional SDE-Net: Generation of Time Series Data with Long-term Memorycited by 9
  37. 2024Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signalscited by 9
  38. 2021Continuous-Depth Neural Models for Dynamic Graph Predictioncited by 7

50 most cited of 147 All 147 (JSON)