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Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching

arXiv 1807.05748 ↗First posted 16 Jul 2018stat.ML cs.LGcited by 23

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Abstract (arXiv)

We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time increments and arbitrary sparseness, which is in contrast with gradient matching that does not optimize simulated responses. We formulate sensitivity equations for learning and demonstrate that our general stochastic distribution optimisation leads to robust and efficient learning of SDE systems.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Jul 2018.

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Citing papers per year: 2021: 7; 2022: 2; 2023: 5; 2024: 3; 2025: 4; 2026: 2.

23 papers.

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  1. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 37
  2. 2023Learning Stochastic Dynamical System via Flow Map Operatorcited by 24
  3. 2022One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernelscited by 15
  4. 2021Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equationcited by 14
  5. 2021Learning stochastic dynamical systems with neural networks mimicking the Euler-Maruyama schemecited by 10
  6. 2023Variational Gaussian Process Diffusion Processescited by 10
  7. 2024Modeling Unknown Stochastic Dynamical System Subject to External Excitationcited by 7
  8. 2024Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systemscited by 5
  9. 2024Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equationscited by 4
  10. 2021Learning particle swarming models from data with Gaussian processescited by 3
  11. 2021Robust and Scalable SDE Learning: A Functional Perspectivecited by 3
  12. 2022Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equationscited by 3
11 more
  1. 2025Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Pathscited by 3
  2. 2023Learning Collective Behaviors from Observationcited by 2
  3. 2023Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structurescited by 2
  4. 2023Geometric path augmentation for inference of sparsely observed stochastic nonlinear systemscited by 1
  5. 2025Nonparametric learning of stochastic differential equations from sparse and noisy datacited by 1
  6. 2021Traversing Time with Multi-Resolution Gaussian Process State-Space Modelscited by 0
  7. 2021The Past as a Stochastic Processcited by 0
  8. 2025The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equationscited by 0
  9. 2025Data-driven Learning of Interaction Laws in Multispecies Particle Systems with Gaussian Processes: Convergence Theory and Applicationscited by 0
  10. 2026Data-driven Effective Modeling of Stochastic Chemical Reaction Networkscited by 0
  11. 2026Simulation-Free Learning of GP-SDEs from Irregular Observationscited by 0