发表机构
School of Mathematical Sciences, SCMS, and SCAM, Fudan University; Research Institute of Intelligent Complex Systems, Fudan University; Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen; Shanghai Artificial Intelligence Laboratory; MOE Frontiers Center for Brain Science and State Key Laboratory of Medical Neurobiology, Fudan University（复旦大学数学科学学院; 复旦大学智能复杂系统研究院; 阿伯丁大学国王学院复杂系统与数学生物学研究所; 上海人工智能实验室; 复旦大学脑科学前沿中心暨医学神经生物学国家重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出神经动力学迁移学习（NDTL）框架，从成对父动力系统创造具有指定动力学的新系统，保留关键特征并生成新动力学，应用于分类、食物链模型、流行病学模型及图像加密。
AI 中文摘要
数据驱动的机器学习已为从观测中重构非线性动力系统建立了坚实基础，主要目的为预测和控制。然而，现有的大多数工作集中于恢复特定的观测动力学，而非新动力学的生成性综合。受图像融合和风格迁移的启发，我们引入了一个称为神经动力学迁移学习（NDTL）的神经网络框架，用于从成对的父非线性动力系统中创建具有指定动力学的新系统。通过计算基本动力学特征，包括固有维数、Kaplan-Yorke维数、不变测度统计量和Lyapunov谱，我们证明了NDTL在生成新动力学的同时，保留了从父模型继承的关键特征。除这些验证示例外，NDTL还引入了动力学分类的标准，在Hastings-Powell食物链模型中创造了稳定的振荡共存，生成了可解释的流行病学模型，并为图像加密提供了混沌源。
英文摘要
Data-driven machine learning has established a robust foundation for reconstructing nonlinear dynamical systems from observations, primarily for the purposes of forecasting and control. However, most existing efforts focus on recovering specific observed dynamics rather than the generative synthesis of new ones. Inspired by image fusion and style transfer, we introduce a neural network framework termed Neural Dynamical Transfer Learning (NDTL) to create new systems with prescribed dynamics from pairs of parent nonlinear dynamical systems. By computing fundamental dynamical signatures, including the intrinsic dimension, the Kaplan-Yorke dimension, the invariant measure statistics, and the Lyapunov spectrum, we demonstrate that NDTL preserves key features inherited from the parent models while simultaneously generating novel dynamics. Beyond these validation examples, NDTL induces a criterion for dynamics classification, creates stable oscillatory coexistence in the Hastings-Powell food chain model, produces interpretable epidemiological models, and provides a chaotic source for image encryption.
