Training time series data with non time series models

Given time series data, for instance features $$x_1(t), x_2(t),\dots, x_N(t)$$ and targets $$y_1(t), y_2(t), \dots, y_M(t)$$, I want to build an ML model that learns the functional relationship between the features and the targets. $$\textbf{Note that my goal is not predicting the future, but only understanding the function}$$ $$\mathbf{y}=f(\mathbf{x})$$.

From my tiny knowledge on deep learning, I know that there are models like (GRU, LSTM neural networks that are powerful for sequences) and predicting the future. However, since I am interested only in the functional relationship, I wonder whether there are other simpler models (for instance simple feed forward neural networks or anything else) that are capable of accomplishing what I want and whether they are suitable for time series data.