Neural network interpolation of exchange-correlation functional

Abstract

Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown. Therefore, the essential part of DFT success is based on the progress in the development of XC approximations. Traditionally, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo numerical calculations. However, there is no consistent and general scheme of XC interpolation and functional representation. Many different developed parametrizations mainly utilize a number of phenomenological rules to construct a specific XC functional. In contrast, the neural network (NN) approach can provide a general way to parametrize an XC functional without any a priori knowledge of its functional form. In this work, we develop NN XC functionals and prove their applicability to 3-dimensional physical systems. We show that both the local density approximation (LDA) and generalized gradient approximation (GGA) are well reproduced by the NN approach. It is demonstrated that the local environment can be easily considered by changing only the number of neurons in the first layer of the NN. The developed NN XC functionals show good results when applied to systems that are not presented in the training/test data. The generalizability of the formulated NN XC framework leads us to believe that it could give superior results in comparison with traditional XC schemes provided training data from high-level theories such as the quantum Monte Carlo and post-Hartree-Fock methods.

Theory-Guided Discovery of Novel Materials

“…The popularity of ML technique in the material science community is attributed to its computing speed and higher prediction accuracy as compared to conventional simulation methods. Recent studies have shown that ML methods can be used to design density functionals − that can provide an alternate route for the DFT approach. By using the ML methods one can directly learn from the electron charge density and completely bypass solving the Kohn–Sham equations, thus enabling the evaluation of the total energy and other properties with far less computational cost than DFT.…”

CIDER: An Expressive, Nonlocal Feature Set for Machine Learning Density Functionals with Exact Constraints

“…One could use a neural network (NN) to learn the features from the raw density distribution in real space, but training features this way is data intensive, with 10 5 -10 6 training points used in recent works. 39,40 In addition, these NNs rely on a specific grid structure over which convolutions are performed, which could impede their use in realistic production calculations. Alternatively, one could project the density or density matrix onto atomic basis sets, as is done in NeuralXC and DeePKS, 13,14 but these two models do not incorporate any physical constraints into the features, making it infeasible to incorporate exact constraints into the model itself.…”

Application of neural network for exchange-correlation functional interpolation

“…NN was first utilized as a functional form for XC potential by Tozer et al [20]. After that, several studies have been addressed the possibility of using NN to approximate XC functionals form [21][22][23][24][25][26]. Work by Nagai and co-authors [22] is especially worthy of note.…”