mlsanityData to 14 Oct 2026

Learning unknown ODE models with Gaussian processes

arXiv 1803.04303 ↗First posted 12 Mar 2018stat.MLcited by 54

Not on the map. Why?

Abstract (arXiv)

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model's capabilities to infer dynamics from sparse data and to simulate the system forward into future.

Key facts. Cited by 54 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Mar 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 9; 2022: 7; 2023: 12; 2024: 7; 2025: 12; 2026: 7.

54 papers.

Sort:

By area:

  1. 2021Neural graphical modelling in continuous-time: consistency guarantees and algorithmscited by 42
  2. 2021Continuous-Time Model-Based Reinforcement Learningcited by 41
  3. 2023Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Seriescited by 29
  4. 2025SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equationscited by 23
  5. 2022AutoIP: A United Framework to Integrate Physics into Gaussian Processescited by 20
  6. 2023Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEscited by 18
  7. 2021Variational multiple shooting for Bayesian ODEs with Gaussian processescited by 15
  8. 2021Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equationcited by 14
  9. 2021Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy datacited by 13
  10. 2024Zero-shot Imputation with Foundation Inference Models for Dynamical Systemscited by 13
  11. 2022Continual Learning from Demonstration of Robotics Skillscited by 12
  12. 2021Structure-preserving Gaussian Process Dynamicscited by 9
38 more
  1. 2023Sparse Variational Student-t Processescited by 8
  2. 2023Free-Form Variational Inference for Gaussian Process State-Space Modelscited by 7
  3. 2023Bayesian Gaussian Process ODEs via Double Normalizing Flowscited by 7
  4. 2024Learning Governing Equations of Unobserved States in Dynamical Systemscited by 7
  5. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
  6. 2023Uncertainty and Structure in Neural Ordinary Differential Equationscited by 6
  7. 2022Learning Interacting Dynamical Systems with Latent Gaussian Process ODEscited by 5
  8. 2023Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernelscited by 5
  9. 2025Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutionscited by 5
  10. 2022Learning nonparametric ordinary differential equations from noisy datacited by 4
  11. 2023Symbolic Regression on Sparse and Noisy Data with Gaussian Processescited by 4
  12. 2024Machine Learning for Predicting Chaotic Systemscited by 4
  13. 2021Learning particle swarming models from data with Gaussian processescited by 3
  14. 2022The Normalized Cross Density Functional: A Framework to Quantify Statistical Dependence for Random Processescited by 3
  15. 2023Exact Inference for Continuous-Time Gaussian Process Dynamicscited by 3
  16. 2024System-Aware Neural ODE Processes for Few-Shot Bayesian Optimizationcited by 3
  17. 2024Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketchingcited by 3
  18. 2026Foundation Inference Models for Ordinary Differential Equationscited by 3
  19. 2022The Past Does Matter: Correlation of Subsequent States in Trajectory Predictions of Gaussian Process Modelscited by 2
  20. 2023Learning Collective Behaviors from Observationcited by 2
  21. 2023Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structurescited by 2
  22. 2024Sparse Variational Student-t Processes for Heavy-tailed Modelingcited by 2
  23. 2025Data-efficient Kernel Methods for Learning Hamiltonian Systemscited by 2
  24. 2025Causal Structure Learning for Dynamical Systems with Theoretical Score Analysiscited by 2
  25. 2021Approximate Latent Force Model Inferencecited by 1
  26. 2023Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformerscited by 1
  27. 2025Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systemscited by 1
  28. 2025Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Datacited by 1
  29. 2025Learning solutions of parameterized stiff ODEs using Gaussian processescited by 1
  30. 2021MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamicscited by 0
  31. 2022A dynamical systems based framework for dimension reductioncited by 0
  32. 2025BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systemscited by 0
  33. 2025Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processescited by 0
  34. 2025Towards Foundation Inference Models that Learn ODEs In-Contextcited by 0
  35. 2025Data-driven Learning of Interaction Laws in Multispecies Particle Systems with Gaussian Processes: Convergence Theory and Applicationscited by 0
  36. 2025CODE: A global approach to ODE dynamics learningcited by 0
  37. 2026Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunitiescited by 0
  38. 2026EVIL: Evolving Interpretable Algorithms for Zero-Shot Inference on Event Sequences and Time Series with LLMscited by 0

50 most cited of 54 All 54 (JSON)