  We develop a combined theoretical and experimental method for estimating the
amount of heating that occurs in metallic nanoparticles that are being imaged
in an electron microscope. We model the thermal transport between the
nanoparticle and the supporting material using molecular dynamics and
eqivariant neural network potentials. The potentials are trained to Density
Functional Theory (DFT) calculations, and we show that an ensemble of
potentials can be used as an estimate of the errors the neural network make in
predicting energies and forces. This can be used both to improve the networks
during the training phase, and to validate the performance when simulating
systems too big to be described by DFT. The energy deposited into the
nanoparticle by the electron beam is estimated by measuring the mean free path
of the electrons and the average energy loss, both are done with Electron
Energy Loss Spectroscopy (EELS) within the microscope. In combination, this
allows us to predict the heating incurred by a nanoparticle as a function of
its size, its shape, the support material, and the electron beam energy and
intensity.
