Applying Machine Learning to Measure Chaos (IMAGE)
Caption
FIG. 1. (a) The attractor of the Ikeda map and a partial trajectory. States colored blue (orange) are measured as outcome A (B). The proposed method optimizes the measurement of a chaotic system using artificial neural networks that apply an IB and vector quantization (VQ) to each continuous-valued state. (b) The space of possible discrete measurements visualized in terms of the entropy of a single measurement H(U) and the rate of entropy production in the infinite duration limit h∞(U). The entropy rate of any partition is upper bounded by H(U) and the metric entropy hKS (dashed lines). The blue point corresponds to the partition in (a) that was optimized with the proposed method. The black points correspond to measurements parametrized by neural networks with random weights. Error bars on the entropy rates are within the markers.
Credit
Dani Bassett, Kieran Murphy
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License
CC BY-NC-SA