Neural Network Representations of Multiphase Equations of State

TL;DR

This paper introduces two deep learning approaches for modeling equations of state that respect thermodynamic laws and phase transitions, offering flexible, accurate, and physically consistent tools for scientific applications.

Contribution

It proposes novel neural network methods that guarantee thermodynamic consistency and phase transition modeling, improving upon traditional analytic models.

Findings

Both methods satisfy thermodynamic laws over large regions.

The models effectively incorporate phase transitions.

They can be used standalone or to refine existing models.

Abstract

Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either "from scratch" to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, and highlight their advantages and shortcomings.