An inverse mapping approach for process systems engineering using automatic differentiation and the implicit function theorem
An inverse mapping approach for process systems engineering using automatic differentiation and the implicit function theorem
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DOI：
10.1002/aic.18119
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发表时间：
2023-04
期刊：
影响因子：
3.7
通讯作者：
V. Alves;J. Kitchin;F. Lima
中科院分区：
文献类型：
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作者：
V. Alves;J. Kitchin;F. Lima
该工作的目的是提出一种新的方法来解决从输出空间到输入空间的反问题，使用自动微分结合隐函数定理和路径积分方案。在过程系统工程(PSE)和科学、技术、工程和数学(STEM)中解决反问题的一种常见方法是使用非线性规划(NLP)工具，当基础过程模型的复杂性和维度都增加时，这可能会变得计算昂贵。该方法利用稳健自动微分包的最新进展，通过积分给定过程的控制微分方程组来计算输入空间区域。这种计算是基于来自输出空间的初始起点来执行的，并且与使用基于NLP的方法来获得逆映射相比，能够保持精度并减少计算时间。用该方法研究了两个非线性案例，即连续搅拌釜式反应器(CSTR)和膜反应器，用于天然气转化为增值化学品，并与(I)广泛(蛮力)搜索正向映射和(Ii)使用NLP求解器获得逆映射进行了比较。结果表明，新方法与经典方法相吻合，计算时间和复杂度大大降低，为反问题的求解开辟了新的方向。
The objective in this work is to propose a novel approach for solving inverse problems from the output space to the input space using automatic differentiation coupled with the implicit function theorem and a path integration scheme. A common way of solving inverse problems in process systems engineering (PSE) and in science, technology, engineering and mathematics (STEM) in general is using nonlinear programming (NLP) tools, which may become computationally expensive when both the underlying process model complexity and dimensionality increase. The proposed approach takes advantage of recent advances in robust automatic differentiation packages to calculate the input space region by integration of governing differential equations of a given process. Such calculations are performed based on an initial starting point from the output space and are capable of maintaining accuracy and reducing computational time when compared to using NLP‐based approaches to obtain the inverse mapping. Two nonlinear case studies, namely a continuous stirred tank reactor (CSTR) and a membrane reactor for conversion of natural gas to value‐added chemicals are addressed using the proposed approach and compared against: (i) extensive (brute‐force) search for forward mapping and (ii) using NLP solvers for obtaining the inverse mapping. The obtained results show that the novel approach is in agreement with the typical approaches, while computational time and complexity are considerably reduced, indicating that a new direction for solving inverse problems is developed in this work.