提出新型神经噪声模型，让生成时间序列更好保留记忆特征。
Nansde-net: A neural sde framework for generating time series with memory
- 用神经网络定义核函数，构造可兼容伊藤积分的带记忆噪声
- 在合成与真实数据上均优于或媲美已有模型，能同时捕捉长短记忆
- 适合需要精准建模时序依赖的科研与工程场景
长短期记忆特性的时间序列建模是众多科学与工程领域的基础挑战。尽管分数布朗运动常被用作噪声源以捕捉记忆效应，但其与伊藤微积分不兼容，限制了其在神经随机微分方程（SDE）框架中的应用。本文提出一类新型噪声——神经网络核ARMA型噪声（NA-noise），这是一种基于伊藤过程的替代方案，可同时捕捉长短期记忆行为。该噪声的核函数由神经网络参数化，并以乘积形式分解以保持马尔可夫性。基于此噪声，我们构建了NANSDE-Net，一种扩展神经SDE的生成模型。我们在温和条件下证明了解的存在性与唯一性，并推导出高效的反向传播训练方案。在合成与真实数据集上的实验表明，NANSDE-Net在重现数据的长短期记忆特征方面表现优异，优于或媲美分数阶SDE-Net，同时在伊藤微积分框架下保持计算可行性。
原文摘要 · Abstract (English)
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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