Related papers: Automatic Differentiation for the Direct Minimizat…
It has recently been shown that configuration state functions (CSF) with local orbitals can provide a compact reference state for low-spin open-shell electronic structures, such as antiferromagnetic states. However, optimizing a low-spin…
In quantum chemistry, self-consistent field (SCF) algorithms define a nonlinear optimization problem, with both continuous and discrete components. In this work, we derive Hartree-Fock-inspired SCF algorithms that can be exactly written as…
Minimisation of discrete energies defined over factors is an important problem in computer vision, and a vast number of MAP inference algorithms have been proposed. Different inference algorithms perform better on factor graph models (GMs)…
In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works,…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
The adaptively compressed exchange (ACE) method provides an efficient way for solving Hartree-Fock-like equations in quantum physics, chemistry, and materials science. The key step of the ACE method is to adaptively compress an operator…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…
The crucial step in density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) is to decide whether the density produced by the density functional for a specific calculation is erroneous and hence should be replaced by, in this…
We report Hartree-Fock (HF) based pseudopotentials suitable for plane-wave calculations. Unlike typical effective core potentials, the present pseudopotentials are finite at the origin and exhibit rapid convergence in a plane-wave basis;…
The Hartree-Fock-RPA approach is applied to the 1D anti-ferromagnetic Heisenberg model in the Jordan-Wigner representation. Somewhat contrary to expectation, this leads to reasonable results for spectral functions and sum rules in the…
Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded…
A practical electronic structure method in which a two-body functional is the fundamental variable is constructed. The basic formalism of our method is equivalent to Hartree-Fock density matrix functional theory [M. Levy in {\it Density…
We investigate the Hartree-Fock solutions to H2 in a minimal basis. We note the properties of the solutions and their disappearance with geometry and propose a new method, Holomorphic Hartree-Fock theory, where we modify the SCF equations…
The expensive cost of computing exact exchange in periodic systems limits the application range of density functional theory with hybrid functionals. To reduce the computational cost of exact change, we present a range-separated algorithm…
In this note we derive the backward (automatic) differentiation (adjoint [automatic] differentiation) for an algorithm containing a conditional expectation operator. As an example we consider the backward algorithm as it is used in Bermudan…
A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…
Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…