Related papers: Revisiting the machine-learning density functional…
Deep learning methods are known to generalize well from training to future data, even in an overparametrized regime, where they could easily overfit. One explanation for this phenomenon is that even when their *ambient dimensionality*,…
Density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard corrections to treat strongly correlated…
We present a machine learning (ML) method for predicting electronic structure correlation energies using Hartree-Fock input.The total correlation energy is expressed in terms of individual and pair contributions from occupied molecular…
One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
A density-matrix formalism is developed based on the one-particle density-matrix of a single-determinantal reference-state. The v-representable problem does not appear in the proposed method, nor the need to introduce functionals defined by…
We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of the monoclinic organic molecular crystal $\beta$-HMX in the geometrical nonlinear regime. A filtered molecular…
Deep neural networks (DNN) with a huge number of adjustable parameters remain largely black boxes. To shed light on the hidden layers of DNN, we study supervised learning by a DNN of width $N$ and depth $L$ consisting of $NL$ perceptrons…
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…
We explore the application of computer vision and machine learning (ML) techniques to predict material properties (e.g. compressive strength) based on SEM images. We show that it's possible to train ML models to predict materials…
A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the…
Realizing large materials models has emerged as a critical endeavor for materials research in the new era of artificial intelligence, but how to achieve this fantastic and challenging objective remains elusive. Here, we propose a feasible…
We construct and apply an exchange-correlation functional for the one-dimensional Hubbard model. This functional has built into it the Luttinger-liquid and Mott-insulator correlations, present in the Hubbard model, in the same way in which…
Predicting the mean-field Hamiltonian matrix in density functional theory is a fundamental formulation to leverage machine learning for solving molecular science problems. Yet, its applicability is limited by insufficient labeled data for…
In this work we propose an artificial neural network functional to the ground-state energy of fermionic interacting particles in homogeneous chains described by the Hubbard model. Our neural network functional was proven to has an excellent…
This paper studies double/debiased machine learning (DML) methods applied to weakly dependent data. We allow observations to be situated in a general metric space that accommodates spatial and network data. Existing work implements…
We introduce machine learning (ML) models that predict the electronic structure of materials across a wide temperature range. Our models employ neural networks and are trained on density functional theory (DFT) data. Unlike most other ML…
Machine Learning (ML) plays an increasingly important role in the discovery and design of new materials. In this paper, we demonstrate the potential of ML for materials research using hard-magnetic phases as an illustrative case. We build…
We study the loss surface of DNNs with $L_{2}$ regularization. We show that the loss in terms of the parameters can be reformulated into a loss in terms of the layerwise activations $Z_{\ell}$ of the training set. This reformulation reveals…
The strength of machine learning models stems from their ability to learn complex function approximations from data; however, this strength also makes training deep neural networks challenging. Notably, the complex models tend to memorize…