  We design a neural network based on a single spin-torque vortex
nano-oscillator (STVO) multiplexed in time. The behavior of the STVO is
simulated with an improved ultra-fast and quantitative model based on the
Thiele equation approach. Different mathematical and numerical adaptations are
brought to the model in order to increase the accuracy and the speed of the
simulations. We demonstrate the high added value and adaptability of such a
neural network through the resolution of three standard machine learning tasks
in the framework of reservoir computing. The first one is a task of waveform
(sines and squares) classification. We show the ability of the system to
effectively classify waveforms with high accuracy and low root-mean-square
error thanks to the intrinsic short-term memory of the device. Given the high
throughput of the simulations, two innovative parametric studies on the
intensity of the input signal and the level of noise in the system are
performed to demonstrate the value of our new models. The efficiency of our
system is then tested during a speech recognition task on the TI-46 dataset and
shows the agreement between the new models and the corresponding experimental
measurements. Finally, we use our STVO-based neural network to perform image
recognition on the MNIST dataset. State-of-the-art performances are
demonstrated, and the interest of using the STVO dynamics as an activation
function is highlighted. These results support and facilitate the future
development of neuromorphic STVO-based hardware for energy-efficient machine
learning.
