Figure 2

(a) Estimation of \(\beta\) from simulated time series of spins, generated with a KIM with piecewise constant \(\beta\) (black line). The \(\beta (t)\) estimated with the DyNoKIM (yellow dots) over 30 simulations is consistently close to the true value. A sample estimated trajectory is shown in darker color. (b) Estimation of J under model misspecification. We simulate 60 time series generated with a KIM and \(\beta (t) = 1 + \mathcal {K} \sin (\omega t)\), \(\omega = 2\pi /300\), \(T=3000\), \(N=30\), \(J_{ij} \sim \mathcal {N}(0, 1/\sqrt{N})\), \(h_i = 0 \; \forall \, i\), then estimate the DyNoKIM. The main panel shows the distribution of the coefficient of a linear regression between the estimated and true J values, using the KIM and a DyNoKIM. Insets show example scatter plots of the true J values (x axis) and the estimated values (y axis) using the standard KIM (yellow points) or the DyNoKIM (purple crosses).