# Robust and Scalable SDE Learning: A Functional Perspective

arXiv: https://arxiv.org/abs/2110.05167 · HTML: https://mlsanity.com/paper/2110.05167/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 11 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching](https://mlsanity.com/paper/1807.05748/) (2018)
- [Approximate Bayes learning of stochastic differential equations](https://mlsanity.com/paper/1702.05390/) (2017)
- [Laplace based approximate posterior inference for differential equation models](https://mlsanity.com/paper/1607.07203/) (2016)
- [Stochastic turbulence modeling in RANS simulations via Multilevel Monte Carlo](https://mlsanity.com/paper/1811.00872/) (2018)

## Built on by (most cited first, 3 of 3)

- [Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processes](https://mlsanity.com/paper/2404.09402/) (2024)
- [Neural Langevin Dynamics: towards interpretable Neural Stochastic Differential Equations](https://mlsanity.com/paper/2211.09537/) (2022)
- [Mitigating Bias in Low-SNR Financial Reinforcement Learning via Quantum Representations](https://mlsanity.com/paper/2606.10448/) (2026)

## Abstract (arXiv)

Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and other flexible function approximators. Despite these advances, learning remains computationally expensive due to the sequential nature of SDE integrators. In this work, we propose an importance-sampling estimator for probabilities of observations of SDEs for the purposes of learning. Crucially, the approach we suggest does not rely on such integrators. The proposed method produces lower-variance gradient estimates compared to algorithms based on SDE integrators and has the added advantage of being embarrassingly parallelizable. This facilitates the effective use of large-scale parallel hardware for massive decreases in computation time.