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This note provides additional results on the training process of Neural ODEs on the one-skyrmion system without grain inhomogeneity and the multi-skyrmions system with grain inhomogeneity, using voltage as input. Fig. S 1 a shows the normalized random sine voltage input used in the training process. Figs. S 1 bc show the predicted training output of∆ mz, by Neural ODE (orange dashed curve) and micromagnetic simulation output (blue curve), for the one-skyrmion and the multi-skyrmions system, respectively. Excellent agreement is seen. Fig. S 2 shows the training loss (MSE) of the one-skyrmion system without grain inhomogeneity as a function of iterations, for:

• a different numbers of units Nh in hidden layers. We observe that, in general, the greater Nh is, the faster the training loss converges.

• b different sampling intervals∆ t of the initially observed trajectory y1 (the unit p is equal to 2.5 ps, as in the main body text). These results show that an accurate Neural ODE model can be trained even if the original continuous time series is downsampled, until a certain point in which the neighboring states of the downsampled trajectory lose correlations.

• c different dimensions k of the Neural ODE (with k− 1 being the number of delays). The Neural ODE model can be successfully trained as long as k≥ 2. Generally, the higher the dimension is, the longer time it takes for the model to train.

• d different choices of training optimization algorithms. It is shown that the ADAM and stochastic gradient descent (SGD) methods ensure a quick convergence of the loss function.