Deep Differential System Stability Learning advanced computations from examples
Table 6: Accuracy on the existence and behavior of solutions at infinity.
['Space dimension for  [ITALIC] x', 'Dim 2', 'Dim 3', 'Dim 4', 'Dim 5', 'Dim 6', 'Overall']
In a first series of experiments the model is only trained to predict the existence and behavior of solutions, encoded as a sequence of two Booleans. Overall accuracy is 98.4%. In a second series, we introduce an auxiliary task by adding to the output the frequency bounds F of u0. We observe that this auxiliary task significantly contributes to the stability of the model with respect to hyper-parameters. In particular, without the auxiliary task, the model is very sensitive to the learning rate scheduling and often fails to converge to something better than random guessing. However, in case of convergence, the model reaches the same overall accuracy, with and without auxiliary task.