Physically Consistent Neural Network Models for Equations of State

Material equations of state provide key information to multi-physics simulation codes, like those used to model inertial confinement fusion and high energy density experiments. For complicated real-world materials, discrete tables that combine theory, simulation and experimental data are the current state of practice. However, when interpolating between tabular data points, physical inconsistencies can arise merely due to the interpolation process. In regions of discontinuities, such as around phase transitions, spurious oscillations in the interpolator can become particularly problematic and can even break physical consistency. In this work, we explore the use of neural networks as an efficient global interpolator for tabular equation of state data and develop model architectures that can not only recreate the original tabular data to within a few percent, but also respect phase boundary transitions without spurious oscillation. As a proof of concept, we apply the methodology to materials of interest to nuclear fusion simulations, such as deuterium-tritium mixtures.

 

Prepared by LLNL under Contract DE-AC52-07NA27344. LLNL-ABS-824171.