Related papers: Neural network approximation of regularized densit…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

Density functional theory has become the world's favorite electronic structure method, and is routinely applied to both materials and molecules. Here, we review recent attempts to use modern machine-learning to improve density functional…

The application of density functional theory to nuclear structure is discussed, highlighting the current status of the effective action approach using effective field theory, and outlining future challenges.

In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density…

We propose a method for microscopic calculations of nuclear ground-state properties in the framework of density functional theory. We discuss how the density functional is equivalent to the effective action for the density, thereby…

We examine the necessary and sufficient complexity of neural networks to approximate functions from different smoothness spaces under the restriction of encodable network weights. Based on an entropy argument, we start by proving lower…

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…

A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible…

Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett. \textbf{107}, 163002 (2011)], a recently developed complex-scaled version of ground-state Density Functional Theory (DFT), are studied in detail. The asymptotic…

We propose a natural quantization of a standard neural network, where the neurons correspond to qubits and the activation functions are implemented via quantum gates and measurements. The simplest quantized neural network corresponds to…

We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given $k$ and a target density $\rho$, there exist potentials having $k^{\text{th}}$ bound mixed states which densities…

Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…

The nonrelativistic reduction of the self-consistent covariant density functional theory is realized for the first time with the similarity renormalization group (SRG) method. The reduced nonrelativistic Hamiltonian and densities are…

In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…

Kohn-Sham Density Functional Theory (KS-DFT) provides the exact ground state energy and electron density of a molecule, contingent on the as-yet-unknown universal exchange-correlation (XC) functional. Recent research has demonstrated that…

Weight-sharing is ubiquitous in deep learning. Motivated by this, we propose a "weight-sharing regularization" penalty on the weights $w \in \mathbb{R}^d$ of a neural network, defined as $\mathcal{R}(w) = \frac{1}{d - 1}\sum_{i > j}^d |w_i…

Deep neural networks (DNNs) can be made hardware-efficient by reducing the numerical precision of the weights and activations of the network and by improving the network's resilience to noise. However, this gain in efficiency often comes at…