In recent years, significant progress in generative AI has highlighted the important role of physics-inspired models that utilize advanced mathematical concepts based on fundamental physics principles to enhance artificial intelligence capabilities. Among these models, those based on diffusion equations have greatly improved image quality. This study aims to explore the potential uses of Maxwell-Boltzmann equation, which forms the basis of the kinetic theory of gases, and the Michaelis-Menten model in Marketing Mix Modelling (MMM) applications. We propose incorporating these equations into Hierarchical Bayesian models to analyse consumer behaviour in the context of advertising. These equation sets excel in accurately describing the random dynamics in complex systems like social interactions and consumer-advertising interactions.

翻译：近年来，生成式人工智能的重大进展凸显了受物理启发的模型的重要作用——这类模型利用基于基础物理原理的先进数学概念来增强人工智能能力。其中，基于扩散方程的模型显著提升了图像质量。本研究旨在探索作为气体动力学理论基础的麦克斯韦-玻尔兹曼方程以及米氏-门滕模型在营销组合建模（MMM）中的潜在应用。我们提出将这些方程纳入分层贝叶斯模型框架，以分析广告情境下的消费者行为。这套方程在准确描述社会互动与消费者-广告交互等复杂系统中的随机动力学方面具有显著优势。