Dynamics Creation through Neural Dynamical Transfer Learning
Abstract
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.
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BibTeX
@misc{ma2026dynamics,
title = {{Dynamics Creation through Neural Dynamical Transfer Learning}},
author = {He Ma and Qiyang Ge and Yu Meng and Celso Grebogi and Wei Lin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09739},
eprint = {2609.09739},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09739},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamics Creation through Neural Dynamical Transfer Learning
AU - He Ma
AU - Qiyang Ge
AU - Yu Meng
AU - Celso Grebogi
AU - Wei Lin
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09739
UR - https://arxiv.org/abs/2609.09739
AB - 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.
ER -