Zanardi Ivan, Venturi Simone, Panesi Marco
Center for Hypersonics and Entry Systems Studies, Department of Aerospace Engineering, University of Illinois Urbana-Champaign, Urbana, 61801, IL, USA.
Sci Rep. 2023 Sep 19;13(1):15497. doi: 10.1038/s41598-023-41039-y.
This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate's architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate's evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-[Formula: see text] scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-[Formula: see text] shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations.
这项工作提出了一种新的基于机器学习（ML）的范式，旨在提高非平衡反应流模拟的计算效率，同时确保符合底层物理规律。该框架通过分层自适应深度学习策略结合降维和神经算子，以学习化学动力学多尺度粗粒度控制方程的解。所提出的代理模型架构被构建为一棵树，叶节点代表单独的神经算子块，其中物理以多个软约束和硬约束的形式嵌入。分层属性有两个优点：（i）它允许通过迁移学习简化训练阶段，从最慢的时间尺度开始；（ii）它通过实现适应性来加速预测步骤，因为代理模型的评估仅限于基于气体局部非平衡程度的必要叶节点。该模型应用于与高超声速飞行相关的化学动力学研究，并在此处针对纯氧气混合物进行了测试。在0 - [公式：见原文] 场景中，所提出的ML框架能够在广泛的初始条件下，以4.5%的最大相对误差自适应预测近三十种物质的动力学。此外，当应用于1 - [公式：见原文] 激波模拟时，与算子分裂积分框架中使用的传统隐式格式相比，该方法显示出1%至4.5%的精度和一个数量级的加速。鉴于本文给出的结果，这项工作为构建一个高效的基于ML的代理模型奠定了基础，该模型与反应性纳维 - 斯托克斯求解器相结合，用于在多维计算流体动力学模拟中准确表征非平衡现象。
