474 research outputs found
A Particle-Based Algorithm for Distributional Optimization on \textit{Constrained Domains} via Variational Transport and Mirror Descent
We consider the optimization problem of minimizing an objective functional,
which admits a variational form and is defined over probability distributions
on the constrained domain, which poses challenges to both theoretical analysis
and algorithmic design. Inspired by the mirror descent algorithm for
constrained optimization, we propose an iterative particle-based algorithm,
named Mirrored Variational Transport (mirrorVT), extended from the Variational
Transport framework [7] for dealing with the constrained domain. In particular,
for each iteration, mirrorVT maps particles to an unconstrained dual domain
induced by a mirror map and then approximately perform Wasserstein gradient
descent on the manifold of distributions defined over the dual space by pushing
particles. At the end of iteration, particles are mapped back to the original
constrained domain. Through simulated experiments, we demonstrate the
effectiveness of mirrorVT for minimizing the functionals over probability
distributions on the simplex- and Euclidean ball-constrained domains. We also
analyze its theoretical properties and characterize its convergence to the
global minimum of the objective functional
Stochastic Estimation of Nuclear Level Density in the Nuclear Shell Model: An Application to Parity-Dependent Level Density in Ni
We introduce a novel method to obtain level densities in large-scale
shell-model calculations. Our method is a stochastic estimation of eigenvalue
count based on a shifted Krylov-subspace method, which enables us to obtain
level densities of huge Hamiltonian matrices. This framework leads to a
successful description of both low-lying spectroscopy and the experimentally
observed equilibration of and states in Ni in a
unified manner.Comment: 13 pages, 4 figure
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