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

• URL: http://arxiv.org/abs/2602.08182v1
• Date: Mon, 09 Feb 2026 00:53:28 GMT
• Title: Nansde-net: A neural sde framework for generating time series with memory
• Authors: Hiromu Ozai, Kei Nakagawa,
• Abstract summary: NANSDE-Net is a generative model that extends Neural SDEs by incorporating NA-noise.<n>We show that NANSDE-Net matches or outperforms existing models, including fractional SDE-Net, in reproducing long- and short-memory features of the data.
• Score: 0.6445605125467572
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Itô 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 Itô-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 Itô calculus framework.

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