  Deep learning has an increasing impact to assist research, allowing, for
example, the discovery of novel materials. Until now, however, these artificial
intelligence techniques have fallen short of discovering the full differential
equation of an experimental physical system. Here we show that a dynamical
neural network, trained on a minimal amount of data, can predict the behavior
of spintronic devices with high accuracy and an extremely efficient simulation
time, compared to the micromagnetic simulations that are usually employed to
model them. For this purpose, we re-frame the formalism of Neural Ordinary
Differential Equations (ODEs) to the constraints of spintronics: few measured
outputs, multiple inputs and internal parameters. We demonstrate with
Spin-Neural ODEs an acceleration factor over 200 compared to micromagnetic
simulations for a complex problem -- the simulation of a reservoir computer
made of magnetic skyrmions (20 minutes compared to three days). In a second
realization, we show that we can predict the noisy response of experimental
spintronic nano-oscillators to varying inputs after training Spin-Neural ODEs
on five milliseconds of their measured response to different excitations.
Spin-Neural ODE is a disruptive tool for developing spintronic applications in
complement to micromagnetic simulations, which are time-consuming and cannot
fit experiments when noise or imperfections are present. Spin-Neural ODE can
also be generalized to other electronic devices involving dynamics.
