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 $B_4C$\ 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.
翻译:国家衡平模型(EOS)是高能量密度物理学、惯性闭合、实验室天体物理学和其他方面研究核心的数值模拟的基础,在这些应用中,需要EOS模型,这些模型涵盖的热力变量范围远远超过数据所具备的范围,使EOS模型的不确定性量化成为一项重大关切。由于为EOS假设的功能形式而选择的模型不确定性,对于EOS的UQ研究来说是一个重大挑战,这种不确定性通常被忽略,因为参数和数据不确定性在不违反EOS物理限制的情况下更容易捕获。在这项工作中,我们引入一个新的EOS统计结构,在自动遵守热力一致性限制的同时,自然捕捉模型不确定性。我们将这一模型应用于现有数据($B_4C$\美元),以便把EOS和Hugoniot的不确定性放在一个最上面,并表明,对热力制约的忽视高估因素估计了在数据可用时的不确定性,而低估了在不超出EOS区域时的不确定性。我们讨论这一方法的扩展,加速了E-Sawa模型的升级,加速了E-GSP的下游模型的作用。