Fig. 4: Demonstration of the capabilities of the transformer-based dynamics reconstruction. | Nature Communications

Fig. 4: Demonstration of the capabilities of the transformer-based dynamics reconstruction.

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

Fig. 4

a Power-law decrease of MSE as the number of training systems k increase. b Scaled frequency \({f}_{s}^{d}\) of training and target systems. c Example of a time series reconstructed by the transformer, compared with linear and spline interpolations, shown in blue, green, and orange, respectively. Traditional interpolation methods fail to recover the time series accurately due to their inability to capture the underlying dynamics. d MSE versus sparsity. While all methods perform similarly under low sparsity, the transformer outperforms the other two methods in reconstructing dynamics when the observational points are sparse. In all cases, 50 independent realizations are used. Error bars and shaded areas represent standard deviations across these realizations.

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