Speaker
Description
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 behaviour, 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 behaviours 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.
