# Neural network stochastic differential equation models with applications to financial data forecasting

arXiv: https://arxiv.org/abs/2111.13164 · HTML: https://mlsanity.com/paper/2111.13164/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 59 references that are in the map.
- First posted on arXiv 25 Nov 2021.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View](https://mlsanity.com/paper/1906.02762/) (2019)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Deep Learning via Dynamical Systems: An Approximation Perspective](https://mlsanity.com/paper/1912.10382/) (2019)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks](https://mlsanity.com/paper/2008.10653/) (2020)

## Built on by (most cited first, 14 of 14)

- [How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equations](https://mlsanity.com/paper/2306.06335/) (2023)
- [Variational Inference for SDEs Driven by Fractional Noise](https://mlsanity.com/paper/2310.12975/) (2023)
- [Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme](https://mlsanity.com/paper/2506.01502/) (2025)
- [Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equations](https://mlsanity.com/paper/2408.06069/) (2024)
- [Multi-task Meta Label Correction for Time Series Prediction](https://mlsanity.com/paper/2303.08103/) (2023)
- [ICODE: Modeling Dynamical Systems with Extrinsic Input Information](https://mlsanity.com/paper/2411.13914/) (2024)
- [Uncertainty Propagation Networks for Neural Ordinary Differential Equations](https://mlsanity.com/paper/2508.16815/) (2025)
- [Continuum Dropout for Neural Differential Equations](https://mlsanity.com/paper/2511.10446/) (2025)
- [Changes from Classical Statistics to Modern Statistics and Data Science](https://mlsanity.com/paper/2211.03756/) (2022)
- [Learning Stochastic Dynamical Systems as an Implicit Regularization with Graph Neural Networks](https://mlsanity.com/paper/2307.06097/) (2023)
- [Orlicz regrets to consistently bound statistics of random variables with an application to environmental indicators](https://mlsanity.com/paper/2310.05168/) (2023)
- [A Method to Improve the Performance of Reinforcement Learning Based on the Y Operator for a Class of Stochastic Differential Equation-Based Child-Mother Systems](https://mlsanity.com/paper/2311.04014/) (2023)
- [Neural Network Learning of Black-Scholes Equation for Option Pricing](https://mlsanity.com/paper/2405.05780/) (2024)
- [A Robust Model-Based Approach for Continuous-Time Policy Evaluation with Unknown L'evy Process Dynamics](https://mlsanity.com/paper/2504.01482/) (2025)

## Abstract (arXiv)

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions are, first, we propose a model called L'evy induced stochastic differential equation network, which explores compounded stochastic differential equations with α-stable L'evy motion to model complex time series data and solve the problem through neural network approximation. Second, we theoretically prove that the numerical solution through our algorithm converges in probability to the solution of corresponding stochastic differential equation, without curse of dimensionality. Finally, we illustrate our method by applying it to real financial time series data and find the accuracy increases through the use of non-Gaussian L'evy processes. We also present detailed comparisons in terms of data patterns, various models, different shapes of L'evy motion and the prediction lengths.