# Nansde-net: A neural sde framework for generating time series with memory

arXiv: https://arxiv.org/abs/2602.08182 · HTML: https://mlsanity.com/paper/2602.08182/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 7 of 7)

- [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 SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [Fractional SDE-Net: Generation of Time Series Data with Long-term Memory](https://mlsanity.com/paper/2201.05974/) (2022)
- [ItoWave: Ito Stochastic Differential Equation Is All You Need For Wave Generation](https://mlsanity.com/paper/2201.12519/) (2022)
- [Neural Stochastic Differential Equations with Change Points: A Generative Adversarial Approach](https://mlsanity.com/paper/2312.13152/) (2023)

## Abstract (arXiv)

Modeling time series with long- or short-memory characteristics is a fundamental challenge in many scientific and engineering domains. While fractional Brownian motion has been widely used as a noise source to capture such memory effects, its incompatibility with Ito calculus limits its applicability in neural stochastic differential equation~(SDE) frameworks. In this paper, we propose a novel class of noise, termed Neural Network-kernel ARMA-type noise~(NA-noise), which is an Ito-process-based alternative capable of capturing both long- and short-memory behaviors. The kernel function defining the noise structure is parameterized via neural networks and decomposed into a product form to preserve the Markov property. Based on this noise process, we develop NANSDE-Net, a generative model that extends Neural SDEs by incorporating NA-noise. We prove the theoretical existence and uniqueness of the solution under mild conditions and derive an efficient backpropagation scheme for training. Empirical results on both synthetic and real-world datasets demonstrate that NANSDE-Net matches or outperforms existing models, including fractional SDE-Net, in reproducing long- and short-memory features of the data, while maintaining computational tractability within the Ito calculus framework.