Related papers: Optimized binning for response function reconstruc…
Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between…
We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett.57, 852 (2002)] to quantum chemical Hamiltonians. This involves two key modifications to the non-spin-adapted DMRG…
A efficient incremental learning algorithm for classification tasks, called NetLines, well adapted for both binary and real-valued input patterns is presented. It generates small compact feedforward neural networks with one hidden layer of…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…
We propose a topology-optimization framework for optimizing finite structures of arbitrary shape by combining density-based methods with level-set approaches. We first optimize regular polygonal structures to suppress the photonic density…
We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific…
This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…
We use a combination of effective field theory and the renormalization group to determine the impact of radiative corrections on the nucleon-nucleon potential and the binding energy of the deuteron. In order to do so, we present a modified…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…
A robust algorithm is proposed to reconstruct the spatial support and the Lam\'e parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of…
In this paper, we study the deep Ritz method for solving the linear elasticity equation from a numerical analysis perspective. A modified Ritz formulation using the $H^{1/2}(\Gamma_D)$ norm is introduced and analyzed for linear elasticity…
Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. In this work, we propose a new parameterization UNEDF2 of…
In this paper, we investigate the reconstruction of a bivariate function from weighted edge integrals on a triangular mesh, a problem of central importance in tomography, computer vision, and numerical approximation. Our approach is based…
In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a…
We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions…
This paper presents reproducing kernel Hilbert spaces method to obtain the numerical solution for partial differential equation constrained optimization problem.
Accessing both amplitude and phase of nuclear response functions is central to fully characterizing light-matter interactions in the X-ray-nuclear regime. Recent work has demonstrated phase retrieval in two-dimensional time- and…
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…
Using the optimized effective potential method in conjunction with the semi-analytical approximation due to Krieger, Li and Iafrate, we have performed fully self-consistent exact exchange-only density-functional calculations for diatomic…