Related papers: Stochastic Algorithms for Self-consistent Calculat…

The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a…

Stochastic computing (SC) is a promising candidate for fault tolerant computing in digital circuits. We present a novel stochastic computing estimation architecture allowing to solve a large group of estimation problems including least…

This paper is focused on the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The algorithm employs sparse grid collocation in the parameter domain…

We present a modification of the $\Delta$SCF method of calculating energies of excited states, in order to make it applicable to resonance calculations of molecules adsorbed on metal surfaces, where the molecular orbitals are highly…

We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…

We present a systematic, quasi-automated methodology for generating electronic models in the framework of second-principles density functional theory (SPDFT). This approach enables the construction of accurate and computationally efficient…

We present the Electronic Tensor Reconstruction Algorithm (ELECTRA) - an equivariant model for predicting electronic charge densities using floating orbitals. Floating orbitals are a long-standing concept in the quantum chemistry community…

We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a…

We introduce an algorithm that can be used to perform stochastic perturbation theory (sPT) to correct any non-linearly parametrized wavefunction that can be optimized using orbital space Variational Monte Carlo (VMC). Although the…

We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The…

We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local…

A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…

In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…

We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…

Stochastic gradient descent (SGD) is a workhorse algorithm for solving large-scale optimization problems in data science and machine learning. Understanding the convergence of SGD is hence of fundamental importance. In this work we examine…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…

Kohn-Sham density functional theory (KS-DFT) has found widespread application in accurate electronic structure calculations. However, it can be computationally demanding especially for large-scale simulations, motivating recent efforts…