Related papers: Dimensionality reduction through tensor factorizat…
Recent progress in nuclear-structure theory has been dramatic. I describe recent and future applications of ab initio calculations and the generator coordinate method to double-beta decay. I also briefly discuss the old and vexing problem…
This work is concerned with multi-dimensional integrals, which are making their appearance in few-body atomic and nuclear physics. It is shown that the relevant two- and three-dimensional integrals can be reduced to one-dimensional form.…
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…
Machine Learning facilitates building a large variety of models, starting from elementary linear regression models to very complex neural networks. Neural networks are currently limited by the size of data provided and the huge…
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…
We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the…
A common approach to modeling dispersion interactions and overcoming the inaccurate description of long-range correlation effects in electronic structure calculations is the use of pairwise-additive potentials, as in the…
Deep neural network (DNN) and auto differentiation have been widely used in computational physics to solve variational problems. When DNN is used to represent the wave function to solve quantum many-body problems using variational…
This review presents some of the challenges in constructing models of atomic nuclei starting from theoretical descriptions of the strong interaction between nucleons. The focus is on statistical computing and methods for analyzing the link…
We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…
While historically many quantum mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a lot of interest has arisen towards quantum effects in…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several {\it ab initio} methods have now emerged that provide nearly exact…
We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of…
The Similarity Renormalization Group (SRG) is investigated as a powerful yet practical method to modify nuclear potentials so as to reduce computational requirements for calculations of observables. The key feature of SRG transformations…
We propose a simple method that allows, in one dimension, to solve exactly a wide class of classical stochastic many-body systems far from equilibrium. For the sake of illustration and without loss of generality, we focus on a model that…
We investigate the problem of periodically modulated strongly interacting neutron matter. We carry out ab initio non-perturbative auxiliary-field diffusion Monte Carlo calculations using an external sinusoidal potential in addition to…