34 research outputs found
Constraining Model Uncertainty in Plasma Equation-of-State Models with a Physics-Constrained Gaussian Process
Equation-of-state (EOS) models underpin numerical simulations at the core of
research in high energy density physics, inertial confinement fusion,
laboratory astrophysics, and elsewhere. In these applications EOS models are
needed that span ranges of thermodynamic variables that far exceed the ranges
where data are available, making uncertainty quantification (UQ) of EOS models
a significant concern. Model uncertainty, arising from the choice of functional
form assumed for the EOS, is a major challenge to UQ studies for EOS that is
usually neglected in favor of parameteric and data uncertainties which are
easier to capture without violating the physical constraints on EOSs. In this
work we introduce a new statistical EOS construction that naturally captures
model uncertainty while automatically obeying the thermodynamic consistency
constraint. We apply the model to existing data for \ to place an upper
bound on the uncertainty in the EOS and Hugoniot, and show that the neglect of
thermodynamic constraints overestimates the uncertainty by factors of several
when data are available and underestimates when extrapolating to regions where
they are not. We discuss extensions to this approach, and the role of GP-based
models in accelerating simulation and experimental studies, defining portable
uncertainty-aware EOS tables, and enabling uncertainty-aware downstream tasks.Comment: 11 pages, 5 figure
Learning thermodynamically constrained equations of state with uncertainty
Numerical simulations of high energy-density experiments require equation of
state (EOS) models that relate a material's thermodynamic state variables --
specifically pressure, volume/density, energy, and temperature. EOS models are
typically constructed using a semi-empirical parametric methodology, which
assumes a physics-informed functional form with many tunable parameters
calibrated using experimental/simulation data. Since there are inherent
uncertainties in the calibration data (parametric uncertainty) and the assumed
functional EOS form (model uncertainty), it is essential to perform uncertainty
quantification (UQ) to improve confidence in the EOS predictions. Model
uncertainty is challenging for UQ studies since it requires exploring the space
of all possible physically consistent functional forms. Thus, it is often
neglected in favor of parametric uncertainty, which is easier to quantify
without violating thermodynamic laws. This work presents a data-driven machine
learning approach to constructing EOS models that naturally captures model
uncertainty while satisfying the necessary thermodynamic consistency and
stability constraints. We propose a novel framework based on physics-informed
Gaussian process regression (GPR) that automatically captures total uncertainty
in the EOS and can be jointly trained on both simulation and experimental data
sources. A GPR model for the shock Hugoniot is derived and its uncertainties
are quantified using the proposed framework. We apply the proposed model to
learn the EOS for the diamond solid state of carbon, using both density
functional theory data and experimental shock Hugoniot data to train the model
and show that the prediction uncertainty reduces by considering the
thermodynamic constraints.Comment: 26 pages, 7 figure
Theoretical and experimental investigation of the equation of state of boron plasmas
We report a theoretical equation of state (EOS) table for boron across a wide
range of temperatures (5.110-5.210 K) and densities
(0.25-49 g/cm), and experimental shock Hugoniot data at unprecedented high
pressures (5608118 GPa). The calculations are performed with full,
first-principles methods combining path integral Monte Carlo (PIMC) at high
temperatures and density functional theory molecular dynamics (DFT-MD) methods
at lower temperatures. PIMC and DFT-MD cross-validate each other by providing
coherent EOS (difference 1.5 Hartree/boron in energy and 5% in pressure)
at 5.110 K. The Hugoniot measurement is conducted at the National
Ignition Facility using a planar shock platform. The pressure-density relation
found in our shock experiment is on top of the shock Hugoniot profile predicted
with our first-principles EOS and a semi-empirical EOS table (LEOS 50). We
investigate the self diffusivity and the effect of thermal and pressure-driven
ionization on the EOS and shock compression behavior in high pressure and
temperature conditions We study the performance sensitivity of a polar
direct-drive exploding pusher platform to pressure variations based on
comparison of the first-principles calculations with LEOS 50 via 1D
hydrodynamic simulations. The results are valuable for future theoretical and
experimental studies and engineering design in high energy density research.
(LLNL-JRNL-748227)Comment: 12 pages, 9 figures, 2 table
Observation and control of shock waves in individual nanoplasmas
In a novel experiment that images the momentum distribution of individual,
isolated 100-nm-scale plasmas, we make the first experimental observation of
shock waves in nanoplasmas. We demonstrate that the introduction of a heating
pulse prior to the main laser pulse increases the intensity of the shock wave,
producing a strong burst of quasi-monochromatic ions with an energy spread of
less than 15%. Numerical hydrodynamic calculations confirm the appearance of
accelerating shock waves, and provide a mechanism for the generation and
control of these shock waves. This observation of distinct shock waves in dense
plasmas enables the control, study, and exploitation of nanoscale shock
phenomena with tabletop-scale lasers.Comment: 8 pages of manuscript, 9 pages of supplemental information, total 17
page