FMEnets：面向非理想平推流反应器设计的流动、物料与能量网络

摘要(中文译文)

我们提出了FMEnets，一种用于非理想平推流反应器设计与分析的物理信息机器学习框架。FMEnets将基本控制方程（流体流动的Navier-Stokes方程、反应组分传输的物料平衡方程以及温度分布的能量平衡方程）集成到一个统一的多尺度网络模型中。该框架由三个相互关联的子网络组成，各子网络配备独立的优化器，能够同时支持正向和逆向问题求解。在正向模式下，FMEnets仅利用入口和出口信息即可预测速度、压力、组分浓度和温度分布。在逆向模式下，FMEnets利用稀疏的多停留时间测量数据同时推断未知动力学参数和状态。FMEnets可以以FME-PINNs形式实现（采用传统多层感知机），也可以以FME-KANs形式实现（基于Kolmogorov-Arnold网络）。全面的消融研究凸显了FMEnets架构在实现准确预测中的关键作用。具体而言，FME-KANs对噪声的鲁棒性强于FME-PINNs，尽管两种表示在无噪声条件下的精度和速度相当。所提出的框架应用于三组不同的反应场景，并与有限元模拟进行了比较。FMEnets有效捕捉了复杂的相互作用，未知动力学参数的相对误差小于2.5%。该新型网络框架不仅为反应器设计与优化提供了一种计算高效的替代方案，还为整合经验关联式、有限且含噪的实验数据以及基本物理方程以指导反应器设计开辟了新途径。

Abstract

We propose FMEnets, a physics-informed machine learning framework for the design and analysis of non-ideal plug flow reactors. FMEnets integrates the fundamental governing equations (Navier-Stokes for fluid flow, material balance for reactive species transport, and energy balance for temperature distribution) into a unified multi-scale network model. The framework is composed of three interconnected sub-networks with independent optimizers that enable both forward and inverse problem-solving. In the forward mode, FMEnets predicts velocity, pressure, species concentrations, and temperature profiles using only inlet and outlet information. In the inverse mode, FMEnets utilizes sparse multi-residence-time measurements to simultaneously infer unknown kinetic parameters and states. FMEnets can be implemented either as FME-PINNs, which employ conventional multilayer perceptrons, or as FME-KANs, based on Kolmogorov-Arnold Networks. Comprehensive ablation studies highlight the critical role of the FMEnets architecture in achieving accurate predictions. Specifically, FME-KANs are more robust to noise than FME-PINNs, although both representations are comparable in accuracy and speed in noise-free conditions. The proposed framework is applied to three different sets of reaction scenarios and is compared with finite element simulations. FMEnets effectively captures the complex interactions, achieving relative errors less than 2.5 % for the unknown kinetic parameters. The new network framework not only provides a computationally efficient alternative for reactor design and optimization, but also opens new avenues for integrating empirical correlations, limited and noisy experimental data, and fundamental physical equations to guide reactor design.

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