Abstract

Inversion is a key method for extracting nonlinear dynamics governed by heterogeneous reaction that occur in parallel in the natural sciences. Therefore, in this study, we propose a Bayesian statistical framework to determine the active reaction pathways using only the noisy observable spatial distribution of the solid phase. In this method, active reaction pathways were explored using a Widely Applicable Bayesian Information Criterion (WBIC), which is used to select models within the framework of Bayesian inference. Plausible reaction mechanisms were determined by maximizing the posterior distribution. This conditional probability is obtained through Markov chain Monte Carlo simulations. The efficiency of the proposed method is then determined using simulated spatial data of the solid phase. The results show that active reaction pathways can be identified from the redundant candidates of reaction pathways. After these redundant reaction pathways were excluded, the controlling factor of the reaction dynamics was estimated with high accuracy.

Graphic Abstract

中文翻译：

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通过贝叶斯变量选择探索非线性平行异质反应路径

摘要

反演是提取由异质反应控制的非线性动力学的关键方法，而异质反应在自然科学中是并行发生的。因此，在这项研究中，我们提出了一种贝叶斯统计框架，仅使用嘈杂的固相的可观察空间分布来确定活性反应途径。在这种方法中，使用广泛适用的贝叶斯信息准则（WBIC）探索了活性反应途径，该准则用于在贝叶斯推断框架内选择模型。通过最大化后验分布来确定合理的反应机制。该条件概率是通过马尔可夫链蒙特卡洛模拟获得的。然后使用固相的模拟空间数据确定所提出方法的效率。结果表明，可以从多余的候选反应途径中识别出活跃的反应途径。在排除了这些多余的反应路径后，可以高精度地估计反应动力学的控制因素。

图形摘要