Year: 2025
Type: article
Abstract: Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior, fractal dimensions, nonlinearity, and strange attractors. In this work, we introduce, for the first time, chaotic learning, a novel multiscale topological paradigm that enables accurate predictions from chaotic systems. We show that seemingly random and unpredictable chaotic dynamics counterintuitively offer unprecedented quantitative predictions. Specifically, we devise multiscale topological Laplacians to embed real-world data into a family of interactive chaotic dynamical systems, modulate their dynamical behaviors, and enable the accurate prediction of the input data. As a proof of concept, we consider 28 datasets from four categories of realistic problems: 10 brain waves, four benchmark protein datasets, 13 single-cell RNA sequencing datasets, and an image dataset, as well as two distinct chaotic dynamical systems, namely the Lorenz and Rossler attractors. We demonstrate chaotic learning predictions of the physical properties from chaos. Our new chaotic learning paradigm profoundly changes the textbook perception of chaos and bridges topology, chaos, and learning for the first time.
Authors: Jian Jiang, Long Chen, Lu Ke, Bozheng Dou, Yueying Zhu, Yazhou Shi, Huahai Qiu, Ben-gong Zhang, Tianshou Zhou, Guo-Wei Wei
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Awards: G2551766503, G3641357265, Synergistic integration of topology and machine learning for the predictions of protein-ligand binding affinities and mutation impacts, G4604530488, Collaborative Research: Integrating Algebraic Topology, Graph Theory, and Multiscale Analysis for Learning Complex and Diverse Datasets, Kinetics-Driven Drug Discovery Using Persistent Homology, Rare-Event Molecular Dynamics and Experimental Data, G6065440738, III: Medium: De Rham-Hodge theory modeling and learning of biomolecular data, G7104333451, AI-based platform for predicting emerging vaccine-escape variants and designing mutation-proof antibodies
OpenAlex ID: W4409087197