Related papers: Riemannian Denoising Model for Molecular Structure…

By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily…

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in…

We present OrbNet Denali, a machine learning model for electronic structure that is designed as a drop-in replacement for ground-state density functional theory (DFT) energy calculations. The model is a message-passing neural network that…

Two types of approaches to modeling molecular systems have demonstrated high practical efficiency. Density functional theory (DFT), the most widely used quantum chemical method, is a physical approach predicting energies and electron…

Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…

We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…

Machine learning based methods have shown potential for optimizing existing molecules with more desirable properties, a critical step towards accelerating new chemical discovery. Here we propose QMO, a generic query-based molecule…

We introduce a computational method for global optimization of structure and ordering in atomic systems. The method relies on interpolation between chemical elements, which is incorporated in a machine learning structural fingerprint. The…

We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function…

Amorphous materials are coming within reach of realistic computer simulations, but new approaches are needed to fully understand their intricate atomic structures. Here, we show how machine-learning (ML)-based techniques can give new,…

We introduce in this paper a manifold optimization framework that utilizes semi-Riemannian structures on the underlying smooth manifolds. Unlike in Riemannian geometry, where each tangent space is equipped with a positive definite inner…

A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the…

Harnessing the recent advance in data science and materials science, it is feasible today to build predictive models for materials properties. In this study, we employ the data of high-throughput quantum mechanics calculations based on…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes…

This study develops identification methods for linear continuous-time symmetric systems, such as electrical network systems, multi-agent network systems, and temperature dynamics in buildings. To this end, we formulate three system…

Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…

In the present work we studied a subfield of Applied Mathematics called Riemannian Optimization. The main goal of this subfield is to generalize algorithms, theorems and tools from Mathematical Optimization to the case in which the…

Most widely used machine learned (ML) potentials for condensed phase applications rely on many-body permutationally invariant polynomial (PIP) or atom-centered neural networks (NN). However, these approaches often lack chemical…

The microscopic center-of-mass (c.m.) correction energies for nuclei ranging from Oxygen to Calcium are systematically calculated by both spherical and axially deformed relativistic mean-field (RMF) models with the effective interaction…