# Fractional SDE-Net: Generation of Time Series Data with Long-term Memory

arXiv: https://arxiv.org/abs/2201.05974 · HTML: https://mlsanity.com/paper/2201.05974/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 16 Jan 2022.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [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)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [The Emergence of Spectral Universality in Deep Networks](https://mlsanity.com/paper/1802.09979/) (2018)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering](https://mlsanity.com/paper/2006.04727/) (2020)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Infinitely deep neural networks as diffusion processes](https://mlsanity.com/paper/1905.11065/) (2019)
- [A Robust Transferable Deep Learning Framework for Cross-sectional Investment Strategy](https://mlsanity.com/paper/1910.01491/) (2019)

## Built on by (most cited first, 9 of 9)

- [Generative Fractional Diffusion Models](https://mlsanity.com/paper/2310.17638/) (2023)
- [Variational Inference for SDEs Driven by Fractional Noise](https://mlsanity.com/paper/2310.12975/) (2023)
- [Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling](https://mlsanity.com/paper/2307.13217/) (2023)
- [New Money: A Systematic Review of Synthetic Data Generation for Finance](https://mlsanity.com/paper/2510.26076/) (2025)
- [Fractional Diffusion Bridge Models](https://mlsanity.com/paper/2511.01795/) (2025)
- [Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimates](https://mlsanity.com/paper/2303.08587/) (2023)
- [Correlated initialization of deep residual networks](https://mlsanity.com/paper/2609.03589/) (2026)
- [CFTM: Continuous time fractional topic model](https://mlsanity.com/paper/2402.01734/) (2024)
- [Nansde-net: A neural sde framework for generating time series with memory](https://mlsanity.com/paper/2602.08182/) (2026)

## Abstract (arXiv)

In this paper, we focus on the generation of time-series data using neural networks. It is often the case that input time-series data have only one realized (and usually irregularly sampled) path, which makes it difficult to extract time-series characteristics, and its noise structure is more complicated than i.i.d. type. Time series data, especially from hydrology, telecommunications, economics, and finance, exhibit long-term memory also called long-range dependency (LRD). The main purpose of this paper is to artificially generate time series with the help of neural networks, making the LRD of paths into account. We propose fSDE-Net: neural fractional Stochastic Differential Equation Network. It generalizes the neural stochastic differential equation model by using fractional Brownian motion with a Hurst index larger than half, which exhibits the LRD property. We derive the solver of fSDE-Net and theoretically analyze the existence and uniqueness of the solution to fSDE-Net. Our experiments with artificial and real time-series data demonstrate that the fSDE-Net model can replicate distributional properties well.