Deep Learning-based prediction of self-energies from ab initio Dynamical Mean-Field Theory for real materials with minimal data sets

Density-functional Theory (DFT) has been the mainstay of solid-state physicists and quantum chemists alike for the better part of several decades to carry out first-principles calculations on solid materials. With the advent of modern machine learning methods DFT-based calculations of energies and forces have been used to train machine learning (ML) models to learn the inter-atomic potential. However, a fatal flaw in DFT-based calculations is the single-particle approximation-based treatment of the exchange-correlation functionals, which severely limits the accuracy of the calculations for materials with open d and f shell elements. ML predictions trained on such limited-accuracy models are also of limited accuracy. In this paper, we demonstrate training sophisticated deep learning based ML models on state-of-the-art ab initio dynamical mean-field theory (DMFT) calculations of self-energies - the part which is entirely missing in DFT - of real materials. Our calculations show that ML-based methods trained on DMFT self-energies, whereby the ML algorithm is trained to recognise the correlation between non-interacting Green's functions obtained from DFT and self-energies from DMFT, allow the ML models to predict self-energies for Green's functions it has never seen before to a very high accuracy. Taking the example of prototypical SrVO₃ a correlated metal, and training on a minimal data set we are able to show that with transfer learning techniques, the ML algorithm is able to predict self energies of CaVO₃, BaVO₃ and very importantly even for SrNbO₃ - which has a completely different element in the same electronic configuration, and is an extremely important material in terms of futuristic device application as transparent conducting oxide. Our study further shows that the transfer learning technique based on pre-trained models on SrVO₃ and SrNbO₃ is able to predict the self-energy of BaNbO₃ when provided with the non-interacting Green's function, without ever having been trained on its self-energy. Our proof-of-concept demonstrates that ML can predict self-energies of unknown materials using small datasets and transfer learning, drastically reducing computational effort. This approach not only enables efficient predictions but also shows that the physics of diverse systems can be captured with minimal data, paving the way for a transformative shift in materials theory.