Fig. 5 | Nature Communications

Fig. 5

From: Chaos as an intermittently forced linear system

Fig. 5

a The linear model obtained from training data (light gray) may be validated on a new test trajectory. Extracting the v r signal as an input to the linear model provides an accurate reconstruction (blue) of the attractor on the test data (black). b Illustration of eigen-time-delay modes in U for the Lorenz system with q = 100 corresponding to a window size of 100 Δt = 0.1 time units. Measurements are convolved with U to obtain v. The U modes resemble polynomials, ordered by energy (i.e., constant, linear, quadratic, etc.). This structure in U is common across most of the examples, and provides a criterion to determine the appropriate number of rows q in H and the rank r