Spatially-Enhanced Temporal Fusion Transformer: Interpretable Multi-Output Prediction for Parametric Dynamical Systems with Time-Varying Inputs

We explore the promising performance of a transformer model in predicting outputs of parametric dynamical systems with external time-varying input signals. The outputs of such systems vary not only with physical parameters but also with external time-varying input signals. Accurately catching the dynamics of such systems is challenging. We have adapted and extended an existing transformer model, called temporal fusion transformer (TFT), for single-output prediction to a multiple-output transformer, named as Spatially-Enhanced Temporal Fusion Transformer (SE-TFT), which is able to predict multiple output responses of these systems. The SE-TFT generalizes the interpretability of the original TFT model. The generalized interpretable attention weight matrix explores not only the temporal correlations in the sequence, but also the interactions between the multiple outputs, providing explanation for the spatial correlation in the output domain. This proposed SE-TFT accurately predicts the sequence of multiple outputs, regardless of the nonlinearity of the system and the dimensionality of the parameter space.