Klaus A. Gernoth

Neural networks that learn to predict probabilities: global models of nuclear stability and decay

Abstract We present a case study in which multilayer feedforward networks are developed to compute probability distributions corresponding to given input patterns. Normalized squashing functions are used for the output neurons, and the Kullback-Leibler relative entropy is adopted as a measure of the departure of computed output distributions from their targets. The evolution of weights is governed by a stochastic back-propagation algorithm based on the entropic cost function. To improve generalization, cycles of pruning and retraining are implemented. The development is framed in terms of the concrete problem of learning and prediction of the systematics of stability and decay of nuclear ground states. For a given input nuclide, characterized by its proton and neutron numbers, a network is required to generate the associated probability distribution over the options of stability and four different modes of decay. With training and test sets provided by the Brookhaven nuclear data facility, a variety of feedforward architectures have been explored, yielding a number of models that demonstrate high quality of performance both in learning and prediction. The nature of the underlying physical problem is such that it would be very difficult to achieve this quality with a global model based on conventional nuclear theory. The work is introduced by a brief survey of other scientific applications of neural networks.

The physics of liquid para-hydrogen

Macroscopic systems of hydrogen molecules exhibit a rich thermodynamic phase behavior. Due to the simplicity of the molecular constituents a detailed exploration of the thermal properties of these boson systems at low temperatures is of fundamental interest. Here, we report theoretical and experimental results on various spatial correlation functions and corresponding distributions in momentum space of liquid para-hydrogen close to the triple point. They characterize the structure of the correlated liquid and provide information on quantum effects present in this Bose fluid. Numerical calculations employ Correlated Density-Matrix (CDM) theory and Path-Integral Monte-Carlo(PIMC)simulations. A comparison of these theoretical results demonstrates the accuracy of CDM theory. This algorithm therefore permits a fast and efficient quantitative analysis of the normal phase of liquid para-hydrogen. We compare and discuss the theoretical results with available experimental data.

Particle Scattering, X-Ray Diffraction, and Microstructure of Solids and Liquids, LNP 610

Scattering from Condensed Matter: A Brief Introduction.- Scattering Studies of Condensed Helium Isotopes.- The One- and Two-Body Densities of Crystalline Matter and Bragg and Diffuse Scattering of Neutrons and X-Rays.- Average Structure vs. Real Structure: Molecular Dynamics Studies of Silica.- Simulation and Theory of Inhomogeneous Liquid Crystals.- Disorder Diffuse Scattering of Crystals and Quasicrystals.- Inelastic Neutron Scattering from Structural Excitations.

STATISTICAL MODELING OF NUCLEAR SYSTEMATICS

Statistical modeling of data sets by neural-network techniques is offered as an alternative to traditional semiempirical approaches to global modeling of nuclear properties. New results are presented to support the position that such novel techniques can rival conventional theory in predictive power, if not in economy of description. Examples include the statistical inference of atomic masses and beta-decay halflives based on the information contained in existing databases. Neural network modeling, as well as other statistical strategies based on new algorithms for artificial intelligence, may prove to be a useful asset in the further exploration of nuclear phenomena far from stability.

QUASICLASSICAL FOURIER PATH INTEGRAL QUANTUM CORRECTION TERMS TO THE KINETIC ENERGY OF INTERACTING QUANTUM MANY-BODY SYSTEMS

A quasiclassical expression for the kinetic energy of interacting quantum many-body systems is derived from the full quantum expression for the kinetic energy as derived by means of the Fourier path integral representation of the canonical many-body density matrix of such systems. This quasiclassical form of the kinetic energy may be cast in the shape of thermodynamic expectation values w.r.t. to the classical Boltzmann distribution of the many-body system, which involves only the many-body interaction in contrast to the full Fourier path integral quantum distribution, which carries contributions also from the many-body kinetic energy operator. The quasiclassical quantum correction terms to the classical Boltzmann equipartition value are valid when the product of temperature and particle mass is large and then lead to significant technical simplifications and increase of speed of Monte Carlo computations of the quantum kinetic energy. The formal findings are tested numerically in quantum Fourier path integral versus classical Monte Carlo simulations.

Radial Distribution and Liquid Structure Function for Liquid Para-Hydrogen at Low Temperatures

We present theoretical results for the radial distribution function g(r) and the static liquid structure function S(k) of liquid para-hydrogen at low temperatures. The results have been obtained via quantum Monte Carlo Path Integral simulations, classical Monte Carlo calculations, and correlated density matrix theory.

EXCITATIONS OF THE SURFACE OF LIQUID 4HE

The surface of liquid 4He at zero temperature and the 4He vapor-liquid interface at temperatures T > 0 are currently the objects of substantial experimental and theoretical interest. Part of this activity concentrates on studying ground state properties, such as the thickness of the 4He surface and interface, for which some experimental data over a range of temperatures are now available.1, 2 Other experimental and theoretical work explores the elementary excitations supported by these inhomogeneous 4He systems. The spectrum of excitations of the surface of liquid 4He in the short wavelength regime has been measured in recent experiments on 4He films adsorbed on a substrate.3, 4 It is well established by earlier measurements5–9 that at long wavelengths the dispersion relation of 4He surface modes may be described correctly by the laws of hydrodynamics.