Fig. 2: Illustration of the transformer-based dynamics reconstruction framework.

a Training (adaptation) phase, where the model is trained on various synthetic chaotic systems, each divided into segments with uniformly distributed sequence lengths Ls and sparsity measure Sm. The data is masked before being input into the transformer, and the ground truth is used to minimize the MSE (mean squared error) loss and smoothness loss with the output. By learning a randomly chosen segment from a random training system each time, the transformer is trained to handle data with varying lengths and different levels of sparsity. b Testing (deployment) phase. The testing systems are distinct from those in the training phase, i.e., the transformer is not trained on any of the testing systems. Given sparsely observed set of points, the transformer is able to reconstruct the dynamical trajectory.