# Identification of Crude Distillation Unit: A Comparison between Neural Network and Koopman Operator
## 1 Introduction  
Crude distillation units (CDUs) play a significant role in the refining sector, responsible for fractionating crude oil into intermediate products that are subsequently processed in downstream units to meet the market specifications. The quality of these intermediate products, primarily influenced by the operating conditions of the CDUs, is crucial for ensuring the quality of the final refinery products [1]. Currently, the oil refining industry is confronting several challenges, including a significant increase in crude oil prices, fluctuations in product demand driven by market dynamics, and specific regulatory constraints imposed on industrial activities [2]. Improving these units may lead to significant improvements in the efficiency and reliability of oil refining processes, ultimately reducing operational costs and increasing overall savings. Developing suitable process control for the CDU is necessary to achieve these objectives. Nevertheless, the existing body of literature primarily focuses on the design of control algorithms, rather than the identification of a CDU to a sufficient accuracy. In recent years, significant advancements in artificial intelligence have facilitated the development of dynamic models through various data-driven techniques, such as polynomial regressions [3; 4; 5; 6], support vector regression (SVR) [7], and Artificial Neural Networks (ANNs). For example, [PERSON] et al. [8] aimed at optimizing product outputs by using an ANN to predict the yield of kerosene, diesel, and atmospheric gas oil. [PERSON] et al. [9] employed an ANN to predict products flow rate that were optimized based on market values. [PERSON] et al. [10] developed an ANN model to optimize energy efficiency by considering crude oil properties, such as boiling point and crude flow rate. Building on this approach, [PERSON] et al. [11] developed a multi-output ANN model to address variationsin crude composition and predict optimum cut-point temperatures, using a hybrid Taguchi and genetic algorithm for more energy-efficient operations. [PERSON] et al. (2012) developed an ANN model for a CDU and employed a Simulated Annealing (SA) optimizer to enhance revenue while reducing energy usage. This work was further extended by the same authors in ([PERSON] et al., 2016; [PERSON] et al., 2017), who incorporated a heat exchanger network model to enhance operational optimization, aiming to boost net profit while adhering to practical constraints. [PERSON] et al. (2015) modeled a CDU process using a wavelet neural network which was combined with the line-up competition algorithm (LCA) for the economic optimization of the CDU operation. More recently, a Long Short-Term Memory network (LSTM) was developed by ([PERSON] et al., 2016) to predict and analyze energy efficiency in the CDU under different operating conditions. A hybrid ANN-SVM model was developed by ([PERSON] et al., 2016) to simulate the performance of the CDU accurately and efficiently within an optimization framework. [PERSON] et al. (2018) developed a hybrid Fuzzy Logic-ANN model to construct a knowledge-based strategy to adapt to different feedstock properties. Bootstrap ANN models were used by [PERSON] and [PERSON] in (2019) and [PERSON] et al. in (2020) to develop a model of a CDU process, with the former authors focusing on energy efficiency and the latter on maximizing the production rate. A comparison between different data-driven models for predicting CDU product properties was investigated by ([PERSON] et al., 2016), including PCA-ResNet, SOM-ResNet, Feedforward Neural Networks (FNNs), Partial Least Squares (PLS), and LASSO. The study concluded that incorporating prior knowledge and employing appropriate dimensionality reduction techniques, such as PCA-ResNet, greatly improved model accuracy. Using machine learning can offer more accurate and sometimes computationally efficient solutions compared to the complex and resource-intensive nature of ANNs ([PERSON] et al., 2016). [PERSON] et al.