Fig. 3: Performance of dynamics reconstruction. | Nature Communications

Fig. 3: Performance of dynamics reconstruction.

From: Bridging known and unknown dynamics by transformer-based machine-learning inference from sparse observations

Fig. 3

a Illustration of reconstruction results for the chaotic food-chain and Lotka–Volterra systems as the testing targets that the transformer has never been exposed to. For each target system, two sets of sparse measurements of different length Ls and sparsity Sr are shown. The trained transformer reconstructs the complete time series in each case. b Color-coded ensemble-averaged MSE values in the parameter plane (Ls, Sr) (b1). Examples of testing MSE versus Sr and Ls only are shown in (b2) and (b3), respectively. c Ensemble-averaged reconstruction stability indicator Rs(MSEc) versus Sr and Ls, the threshold MSE is MSEc = 0.01. d Robustness of dynamics reconstruction against noise: ensemble-averaged MSE in the parameter plane (σ, Sr) (d1) and (σ, Ls) (d2), with σ being the noise amplitude. An example of reconstruction under noise of amplitude σ = 0.1 is shown in (d3). The values of the performance indicators are the result of averaging over 50 independent statistical realizations.

Back to article page