Related papers: Neural Density Functional Theory in Higher Dimensi…

Although the neural network (NN) technique plays an important role in machine learning, understanding the mechanism of NN models and the transparency of deep learning still require more basic research. In this study, we propose a novel…

Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…

Dynamic Textures (DTs) are sequences of images of moving scenes that exhibit certain stationarity properties in time such as smoke, vegetation and fire. The analysis of DT is important for recognition, segmentation, synthesis or retrieval…

The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of…

We present a scheme for investigating arbitrary thermal observables in spatially inhomogeneous equilibrium many-body systems. Extending the grand canonical ensemble yields any given observable as an explicit hyper-density functional.…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

The predictive accuracy of density functional theory (DFT) for alloy formation enthalpies is often limited by intrinsic energy resolution errors, particularly in ternary phase stability calculations. In this work, we present a machine…

Metric and kernel learning are important in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are…

We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an…

Fully convolutional deep neural networks have been asserted to be fast and precise frameworks with great potential in image segmentation. One of the major challenges in training such networks raises when data is unbalanced, which is common…

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…

The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) are re-examined in the light of the recently introduced concept of global stability of…

Soft-thresholding has been widely used in neural networks. Its basic network structure is a two-layer convolution neural network with soft-thresholding. Due to the network's nature of nonlinearity and nonconvexity, the training process…

Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically…

In this work, we present a deep collocation method for three dimensional potential problems in nonhomogeneous media. This approach utilizes a physics informed neural network with material transfer learning reducing the solution of the…

A classical density functional theory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation…

We develop new transfer learning algorithms to accelerate prediction of material properties from ab initio simulations based on density functional theory (DFT). Transfer learning has been successfully utilized for data-efficient modeling in…

The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids at thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when…