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Machine learning model for efficient nonthermal tuning of the charge density wave in monolayer NbSe$_2$

Understanding and controlling the charge density wave (CDW) phase diagram of transition metal dichalcogenides is a long-studied problem in condensed matter physics. However, due to complex involvement of electron and lattice degrees of freedom and pronounced anharmonicity, theoretical simulations of the CDW phase diagram at the density-functional-theory level are often numerically demanding. To reduce the computational cost of first principles modelling by orders of magnitude, we have developed an electronic free energy machine learning model for monolayer NbSe$_2$ that allows changing both electronic and ionic temperatures independently. Our approach relies on a machine learning model of the electronic density of states and zero-temperature interatomic potential. This allows us to explore the CDW phase diagram of monolayer NbSe$_2$ both under thermal and laser-induced nonthermal conditions. Our study provides an accurate estimate of the CDW transition temperature at low cost and can disentangle the role of hot electrons and phonons in nonthermal ultrafast melting process of the CDW phase in NbSe$_2$.