相关论文: A complete OSV-MP2 analytical gradient theory for …

We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying…

We analyze stochastic gradient algorithms for optimizing nonconvex problems. In particular, our goal is to find local minima (second-order stationary points) instead of just finding first-order stationary points which may be some bad…

We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of…

We present the formulation and implementation of an analytical gradient algorithm for extended multiconfiguration quasidegenerate perturbation theory (XMCQDPT2) with the resolvent-fitting approximation by Granovsky. This algorithm is…

Recent results suggest that quantum computers possess the potential to speed up nonconvex optimization problems. However, a crucial factor for the implementation of quantum optimization algorithms is their robustness against experimental…

The high computational scaling with the number of correlated electrons and the size of the basis set is a bottleneck which limits applications of coupled cluster (CC) algorithms. This is particularly so for calculations based on 2- or…

The original formulation (Phys. Rev. Lett. 119, 063002, 2017) of the natural orbital functional - second-order M{\o}ller-Plesset (NOF-MP2) method is based on the MP2 that uses the canonical Hartree-Fock molecular orbitals. The current work…

In this paper, we develop a stochastic set-valued optimization (SVO) framework tailored for robust machine learning. In the SVO setting, each decision variable is mapped to a set of objective values, and optimality is defined via set…

We present an extension of our one-body M{\o}ller-Plesset second-order perturbation (OBMP2) method for open-shell systems. We derived the OBMP2 Hamiltonian through the canonical transformation followed by the cumulant approximation to…

Gradient descent and its variants are widely used in machine learning. However, oracle access of gradient may not be available in many applications, limiting the direct use of gradient descent. This paper proposes a method of estimating…

In condensed matter physics, particularly in perovskite materials, the rotational motion of molecules and ions is associated with important issues such as ion conduction mechanism. Constrained Molecular Dynamics (MD) simulations offer a…

Aiming at optimizing the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary points of the M\"obius energy. The gradients are computed with respect to Sobolev inner…

In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can…

Block tensor decomposition (BTD) and canonical polyadic decomposition (CPD) are combined into a unified $O(N^3)$-scaling framework for second-order perturbation theory (PT2), demonstrated on MP2 and renormalized PT2 (rPT2). BTD constructs…

We present an approach to renormalized second-order Green's function perturbation theory (GF2) which avoids all dependency on continuous variables, grids or explicit Green's functions, and is instead formulated entirely in terms of static…

We develop an alternative formulation in the energy-domain to calculate the second order M{\o}ller-Plesset (MP2) perturbation energies. The approach is based on repeatedly choosing four random energies using a non-separable guiding…

The atomic-to-molecular (HI-to-H$_2$) transition in photodissociation regions (PDRs) has been investigated over the last several decades through analytic and numerical modeling. However, classical PDR models typically assume uniform density…

We propose a projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization, where the objective function is a nested composition of $T$ functions and the constraint set is a closed convex…

The $\Delta \text{NO}$ method for static correlation is combined with second-order M{\o}ller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions…

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…