Density Functional Theory (DFT) in the Kohn-Sham formalism is one of the most widespread methods for simulating microscopic properties in solid-state physics and chemistry. Its main advantage lies in its ability to strike a favorable balance between accuracy and computational cost. The continuous evolution of increasingly efficient numerical techniques has constantly broadened the scope of its applicability.
Among these techniques that can be associated with DFT, machine learning is being used more and more. Today, a very common application consists in producing potentials capable of predicting interactions between atoms using supervised learning models, relying on properties computed by DFT.
The objective of the project proposed as part of this thesis is to use machine learning techniques at a deeper level, notably to predict the electronic density in crystals or molecules. Compared to predicting properties such as forces between atoms, calculating the electronic density presents certain challenges: the electronic density is high-dimensional since it must be calculated throughout all space; its characteristics vary strongly from one material to another (metals, insulators, charge transfer, etc.). Ultimately, this can represent a significant computational cost. There are several options to reduce the dimensionality of the electronic density, such as computing projections or using localization functions.
The final goal of this project is to be able to predict, with the highest possible accuracy, the electronic density, in order to use it as a prediction or as a starting point for calculations of electron-specific properties (magnetism, band structure, for example).
In a first stage, the candidate will be able to implement methods recently proposed in the literature; in a second part of the thesis, it will then be necessary to propose new ideas. Finally, the implemented method will be used to accelerate the prediction of properties of large systems involving charge transfers, such as defect migration in crystals.