Abstract Bayesian analysis provides a framework for the inverse uncertainty quantification (UQ) of combustion kinetic models. As the workhorse of the Bayesian approach, the Markov chain Monte Carlo (MCMC) methods, however, incur a substantial computational cost. In this work, a surrogate model is employed to improve the traditional MCMC algorithm. Specifically, the test errors of three typical surrogate models are compared, namely Polynomial Chaos Expansion (PCE), High Dimensional Model Representation (HDMR) and Artificial Neural Network (ANN); and ANN is shown to be a relatively more efficient surrogate model for the approximation of combustion reaction systems under extensive conditions. An inverse UQ method, which is the combination of the ANN and traditional MCMC method, and as such termed ANN–MCMC, is adopted. The calculation is performed on the methanol oxidation system and a series of ignition delay data are employed to optimize the rate coefficients of the kinetic model. The estimated posterior distributions of the rate coefficients and the model predictions using the ANN–MCMC are compared with the traditional MCMC methods, with the results showing that the ANN–MCMC can significantly reduce the computational cost needed for the MCMC algorithm, especially on the estimation of the posterior distributions of the input parameters. The rejection rate of the samples in a Markov chain is very high, especially for the calculation of the posterior distribution of less sensitive parameters, thus a large number of samples are needed to reach a desired accuracy for traditional MCMC process. While no samples are rejected when training the ANN surrogate model. Therefore, fewer original samples are needed to get a converged ANN surrogate, which can then generate a large number of low-cost ANN samples for a better accuracy of the MCMC process. The errors for the estimated posterior distributions using ANN–MCMC depend on the accuracy of converged ANN surrogates and more accurate results are obtained with improved settings of ANN. The ANN–MCMC is especially suitable to the computational systems when the computational ability is limited.

中文翻译：

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使用人工神经网络促进燃烧动力学模型的贝叶斯分析

摘要 贝叶斯分析为燃烧动力学模型的逆不确定性量化 (UQ) 提供了一个框架。然而，作为贝叶斯方法的主力，马尔可夫链蒙特卡罗 (MCMC) 方法会产生大量的计算成本。在这项工作中，采用代理模型来改进传统的 MCMC 算法。具体比较了三种典型代理模型的测试误差，即多项式混沌扩展（PCE）、高维模型表示（HDMR）和人工神经网络（ANN）；并且 ANN 被证明是一种相对更有效的替代模型，用于近似广泛条件下的燃烧反应系统。采用了一种逆 UQ 方法，它是 ANN 和传统 MCMC 方法的结合，因此称为 ANN-MCMC。对甲醇氧化系统进行计算，并利用一系列点火延迟数据来优化动力学模型的速率系数。将使用 ANN-MCMC 的速率系数的估计后验分布和模型预测与传统的 MCMC 方法进行比较，结果表明 ANN-MCMC 可以显着降低 MCMC 算法所需的计算成本，特别是在估计上输入参数的后验分布。马尔可夫链中样本的拒绝率非常高，特别是对于不太敏感参数的后验分布的计算，因此需要大量样本才能达到传统MCMC过程所需的精度。虽然在训练 ANN 代理模型时没有拒绝任何样本。因此，需要较少的原始样本来获得收敛的 ANN 代理，然后可以生成大量低成本的 ANN 样本，从而提高 MCMC 过程的准确性。使用 ANN-MCMC 估计后验分布的误差取决于收敛的 ANN 代理的准确性，并且通过改进 ANN 设置可以获得更准确的结果。ANN-MCMC 特别适用于计算能力有限的计算系统。