用改进Transformer预测多输出动态系统，还能解释变量间关系。
Spatially-Enhanced Temporal Fusion Transformer: Interpretable Multi-Output Prediction for Parametric Dynamical Systems with Time-Varying Inputs
- 扩展TFT为多输出模型，融合时空关联性
- 在非线性与高维参数下仍保持高精度预测
- 可解释注意力矩阵揭示输出间空间关联
我们研究了Transformer模型在预测具有外部时变输入信号的参数化动力系统输出方面的潜力。此类系统的输出不仅随物理参数变化，还受外部时变输入影响，准确捕捉其动态特性极具挑战。为此，我们对现有的单输出Transformer模型——时间融合变换器（Temporal Fusion Transformer, TFT）进行了适配与扩展，提出一种多输出模型——空间增强时间融合变换器（Spatially-Enhanced Temporal Fusion Transformer, SE-TFT），可预测这些系统的多个输出响应。SE-TFT继承并推广了原TFT模型的可解释性，其广义可解释注意力权重矩阵不仅能捕捉序列中的时间相关性，还能揭示多输出之间的交互关系，提供输出域中空间相关性的解释。该模型在系统非线性及参数空间高维度条件下，仍能精确预测多输出序列。
原文摘要 · Abstract (English)
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.
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