相关论文: A complete OSV-MP2 analytical gradient theory for …
The recently proposed natural orbital functional second-order M{\o}ller-Plesset (NOF-MP2) method is capableof achieving both dynamic and static correlation even for those systems with significant multiconfigurational character. We test its…
In earlier work [J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order N-electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual…
The multi-mode anharmonic Brownian motion model provides a universal framework for simulating molecular vibrations in condensed phases. When vibrational energy surpasses thermal excitation, quantum effects become significant, necessitating…
Decentralized optimization with orthogonality constraints is found widely in scientific computing and data science. Since the orthogonality constraints are nonconvex, it is quite challenging to design efficient algorithms. Existing…
This work studies minimization problems with zero-order noisy oracle information under the assumption that the objective function is highly smooth and possibly satisfies additional properties. We consider two kinds of zero-order projected…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which…
We use energies and forces predicted within response operator based quantum machine learning (OQML) to perform geometry optimization and transition state search calculations with legacy optimizers. For randomly sampled initial coordinates…
We present a novel gradient-free algorithm to solve a convex stochastic optimization problem, such as those encountered in medicine, physics, and machine learning (e.g., adversarial multi-armed bandit problem), where the objective function…
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
Performing accurate large eddy simulations in compressible, turbulent magnetohydrodynamics is more challenging than in non-magnetized fluids due to the complex interplay between kinetic, magnetic and internal energy at different scales.…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…
This paper develops a spatially resolved perturbation theory for singular vectors under high-dimensional separable noise and applies it to data-driven matrix recovery. In the asymptotic regime where the matrix dimensions are proportional…
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…
Our approach is part of the close link between continuous dissipative dynamical systems and optimization algorithms. We aim to solve convex minimization problems by means of stochastic inertial differential equations which are driven by the…
Motivated by the super-diffusivity of self-repelling random walk, which has roots in statistical physics, this paper develops a new perturbation mechanism for optimization algorithms. In this mechanism, perturbations are adapted to the…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
In this paper, we establish the ordinary differential equation (ODE) that underlies the training dynamics of Model-Agnostic Meta-Learning (MAML). Our continuous-time limit view of the process eliminates the influence of the manually chosen…
A high-fidelity finite volume scheme based on the BVD (boundary variation diminishing) concept is proposed in this study to solve the ideal magnetohydrodynamics (MHD) equations. A hybrid spatial reconstruction profile, consisting of a…