Accelerating superconductor discovery through tempered deep learning of
  the electron-phonon spectral function
Jason B. Gibson Ajinkya C. Hire Philip M. Dee Oscar Barrera Benjamin Geisler Peter J. Hirschfeld Richard G. Hennig
Integrating deep learning with the search for new electron-phonon
superconductors represents a burgeoning field of research, where the primary
challenge lies in the computational intensity of calculating the
electron-phonon spectral function, $\alpha^2F(\omega)$, the essential
ingredient of Midgal-Eliashberg theory of superconductivity. To overcome this
challenge, we adopt a two-step approach. First, we compute $\alpha^2F(\omega)$
for 818 dynamically stable materials. We then train a deep-learning model to
predict $\alpha^2F(\omega)$, using an unconventional training strategy to
temper the model's overfitting, enhancing predictions. Specifically, we train a
Bootstrapped Ensemble of Tempered Equivariant graph neural NETworks (BETE-NET),
obtaining an MAE of 0.21, 45 K, and 43 K for the Eliashberg moments derived
from $\alpha^2F(\omega)$: $\lambda$, $\omega_{\log}$, and $\omega_{2}$,
respectively, yielding an MAE of 2.5 K for the critical temperature, $T_c$.
Further, we incorporate domain knowledge of the site-projected phonon density
of states to impose inductive bias into the model's node attributes and enhance
predictions. This methodological innovation decreases the MAE to 0.18, 29 K,
and 28 K, respectively, yielding an MAE of 2.1 K for $T_c$. We illustrate the
practical application of our model in high-throughput screening for high-$T_c$
materials. The model demonstrates an average precision nearly five times higher
than random screening, highlighting the potential of ML in accelerating
superconductor discovery. BETE-NET accelerates the search for high-$T_c$
superconductors while setting a precedent for applying ML in materials
discovery, particularly when data is limited.