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Prior-guided adaptive sampling for unsupervised learning of multi-material Riemann solvers.

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Bibliographic Details
Title: Prior-guided adaptive sampling for unsupervised learning of multi-material Riemann solvers.
Authors: Liu, Ziyan1 (AUTHOR) xul@buaa.edu.cn, Xu, Liang1 (AUTHOR), Feng, Yiwei1 (AUTHOR), Liu, Yaofeng1 (AUTHOR)
Source: Physics of Fluids. Sep2025, Vol. 37 Issue 9, p1-18. 18p.
Subject Terms: *MACHINE learning, *ADAPTIVE sampling (Statistics), *MASS density gradients, *ARTIFICIAL neural networks, *MULTIPHASE flow
Abstract: Machine learning provides a novel and practical approach to solving Riemann problems to model the coupling effects of multi-material flows. However, inaccurate predictions by surrogate models have been observed in regions of significant density differences between fluids. Such a gap limits the broader applicability of those models across diverse initial conditions. In this work, an adaptive sampling method that emphasizes the prior large-error generation mechanism is proposed to enhance the accuracy of unsupervised learning of multi-material Riemann solvers. Through an analysis of the solution strategy, we identify that these inaccuracies stem from the excessive gradients of the physics-constrained function under an extreme density difference. Based on this finding, we formulate a prior distribution suited for unsupervised neural network solvers of multi-material Riemann problems. This distribution guides the adaptive sampling method to focus on critical regions, thereby improving the overall performance of the model and ensuring faster and more accurate convergence of the network training. The proposed method is validated on various initial conditions and demonstrates high accuracy in predicting interfacial pressure and other interfacial states. This work addresses the limitations of previous methods and enhances the adaptability of the physics-constrained neural network Riemann solver to a broader range of computational conditions. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:Machine learning provides a novel and practical approach to solving Riemann problems to model the coupling effects of multi-material flows. However, inaccurate predictions by surrogate models have been observed in regions of significant density differences between fluids. Such a gap limits the broader applicability of those models across diverse initial conditions. In this work, an adaptive sampling method that emphasizes the prior large-error generation mechanism is proposed to enhance the accuracy of unsupervised learning of multi-material Riemann solvers. Through an analysis of the solution strategy, we identify that these inaccuracies stem from the excessive gradients of the physics-constrained function under an extreme density difference. Based on this finding, we formulate a prior distribution suited for unsupervised neural network solvers of multi-material Riemann problems. This distribution guides the adaptive sampling method to focus on critical regions, thereby improving the overall performance of the model and ensuring faster and more accurate convergence of the network training. The proposed method is validated on various initial conditions and demonstrates high accuracy in predicting interfacial pressure and other interfacial states. This work addresses the limitations of previous methods and enhances the adaptability of the physics-constrained neural network Riemann solver to a broader range of computational conditions. [ABSTRACT FROM AUTHOR]
ISSN:10706631
DOI:10.1063/5.0283375