Neural network surrogate models for equations of state

Abstract

Equation of state (EOS) data provide necessary information for accurate multiphysics modeling, which is necessary for fields such as inertial confinement fusion. Here, we suggest a neural network surrogate model of energy and entropy and use thermodynamic relationships to derive other necessary thermodynamic EOS quantities. We incorporate phase information into the model by training a phase classifier and using phase-specific regression models, which improves the modal prediction accuracy. Our model predicts energy values to 1% relative error and entropy to 3.5% relative error in a log-transformed space. Although sound speed predictions require further improvement, the derived pressure values are accurate within 10% relative error. Our results suggest that neural network models can effectively model EOS for inertial confinement fusion simulation applications.

Deep energy-pressure regression for a thermodynamically consistent EOS model

“…A promising solution to build a universal EOS model is to leverage an iFPEOS table of finite size to train an ML model that can recover any missing values in the table and hence explain the wide range of behaviors of deuterium EOS. As some recent efforts in using ML to model EOS [20,21] show, using a neural network (NN) surrogate model to provide EOS information is viable and provides advantages such as saving the memory cost of restoring all EOS tables, providing differentiability for downstream tasks, and accelerating simulations. Another important factor is as aforementioned, that an NN model can provide a universal approximation.…”

Physics-enhanced neural networks for equation-of-state calculations

“…However, machine learning models offer an intriguing path to interpolate EOS data with only minimal physical constraints from the user, and, for example, modern practices in machine learning can be used for more robust error estimation. Applying machine learning techniques to EOS data is still a relatively fresh topic: most of the applications to date focused on uncertainty quantification [75][76][77], although in a recent work [78] the authors built a surrogate EOS model using neural networks.…”

“…Our work has further novelty because, to the best of our knowledge, output from AA calculations has not previously been used to supplement interpolations of first-principles (or alternative sources of high-fidelity) data. Our work is similar in spirit to [78], but it is distinguished by the inclusion of the AA outputs, besides various other differences such as the reference data, the neural network architecture, and the training and evaluation framework.…”