Dayou Yu, Deep Shankar Pandey, J. Hinz, D. Mihaylov, Valentin V. Karasiev, Suxing Hu, Qi Yu
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We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. Our evaluation results show an excellent fit of the EOS table and the predicted values are ready to use for important physics-related tasks.","PeriodicalId":503691,"journal":{"name":"Machine Learning: Science and Technology","volume":"85 3","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Deep Energy-Pressure Regression for a Thermodynamically Consistent EOS Model\",\"authors\":\"Dayou Yu, Deep Shankar Pandey, J. Hinz, D. Mihaylov, Valentin V. Karasiev, Suxing Hu, Qi Yu\",\"doi\":\"10.1088/2632-2153/ad2626\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n In this paper, we aim to explore novel machine learning (ML) techniques to facilitate and accelerate the construction of universal Equation-Of-State (EOS) models with a high accuracy while ensuring important thermodynamic consistency. When applying ML to fit a universal EOS model, there are two key requirements: (1) a high prediction accuracy to ensure precise estimation of relevant physics properties and (2) physical interpretability to support important physics-related downstream applications. We first identify a set of fundamental challenges from the accuracy perspective, including an extremely wide range of input/output space and highly sparse training data. We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. 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引用次数: 0
摘要
在本文中,我们旨在探索新型机器学习(ML)技术,以促进和加速构建高精度的通用状态方程(EOS)模型,同时确保重要的热力学一致性。在应用 ML 拟合通用 EOS 模型时,有两个关键要求:(1) 高预测精度,以确保精确估计相关物理特性;(2) 物理可解释性,以支持重要的物理相关下游应用。我们首先从精度的角度确定了一系列基本挑战,包括极其广泛的输入/输出空间和高度稀疏的训练数据。我们证明,虽然神经网络(NN)模型可以很好地拟合 EOS 数据,但其黑箱性质使其难以提供物理上可解释的结果,导致预测结果在训练范围之外的责任性很弱,并且无法保证满足重要的热力学一致性约束。为此,我们提出了一种有原则的深度回归模型,该模型可以按照元学习的方式进行训练,从而利用稀缺的训练数据高精度地预测所需的量。我们还引入了一种独特设计的基于内核的正则化器,用于准确量化不确定性。利用集合技术来对抗模型过拟合,同时提高预测稳定性。我们还进行了自动区分,以验证是否保持了必要的热力学一致性条件。我们的评估结果表明,EOS 表的拟合效果极佳,预测值可用于重要的物理相关任务。
Deep Energy-Pressure Regression for a Thermodynamically Consistent EOS Model
In this paper, we aim to explore novel machine learning (ML) techniques to facilitate and accelerate the construction of universal Equation-Of-State (EOS) models with a high accuracy while ensuring important thermodynamic consistency. When applying ML to fit a universal EOS model, there are two key requirements: (1) a high prediction accuracy to ensure precise estimation of relevant physics properties and (2) physical interpretability to support important physics-related downstream applications. We first identify a set of fundamental challenges from the accuracy perspective, including an extremely wide range of input/output space and highly sparse training data. We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. Our evaluation results show an excellent fit of the EOS table and the predicted values are ready to use for important physics-related tasks.