# Model Predictive Evolutionary Temperature Control via Neural-Network-Based Digital Twins
## 1 Introduction
Their approach successfully reduced the operating costs of the equipment, while ensuring that thermal comfort constraints were not compromised. In comparison to the fixed set-point (FSP) approach, the NN-augmented MPC achieved cost savings ranging from 6% to 73%, depending on the season. Similarly, [PERSON] et al. [17] investigated the application of an NN in the context of MPC, focusing on temperature control in a stirred tank reactor. [PERSON] et al. [18] used NNs to generate control laws for MPC of voltage-current regulation in DC-DC converters. Similarly, [PERSON] et al. [19] demonstrated that the computation time of MPC can be drastically reduced with an NN controller for real-world robotic systems. In another study, [PERSON] et al. [20] employed an NN in conjunction with MPC to control a simulated depropanizer in Aspen HYSYS, achieving a remarkable 60% reduction in settling time compared to a traditional PID controller. [PERSON] et al. [21] utilized a recurrent neural network (RNN) along with a particle swarm optimization (PSO) to model an industrial paste thickening process. The RNN-based MPC successfully maintained the desired concentration of the paste thickener, even in the presence of severe pump failures. Other RNN-based applications include solving a generic nonconvex control problem [22], optimal policy selection [23], fault diagnosis for HVAC systems [24], theory [25] and application [26] of a generic nonlinear system for open-loop simulations, multi-mode process control of a generic system [27], chemical reactor control [28], crystallization processes [29] annealing furnaces [30], N-tank problems [31] and corn production [32]. [PERSON] et al. [33] very recently introduced a model-based predictive controller that utilized the object map obtained from the convolutional neural network (CNN) detector and light detection and ranging (LIDAR) data to guide an omnidirectional robot to specific positions in a warehouse environment. For a more comprehensive understanding of recent advancements in model predictive control, we recommend consulting several key papers. [PERSON] [34] offers a detailed comparison of different predictive control methods. In the realm of autonomous systems, [PERSON] et al. [35] delve into the realm of data-driven control. For those interested in chemical process systems, [PERSON] and [PERSON] [36] provide a comprehensive exploration. [PERSON] et al. [37] present a holistic view of model predictive control, while [PERSON] et al. [38] explore the integration of machine learning techniques in this context. The literature review on NN-augmented MPC reveals the successful utilization of neural networks as effective approximators in MPC. Recent advancements in deep learning, such as neural networks with memory functions (RNNs) and specialized architectures capable of handling spatial information (CNNs), have further enhanced the representational power of data-driven models. Our contribution introduces a noteworthy progression within the domain of intelligent control strategies, stemmed from the strategic utilization of _ConvLSTM-based_ digital twins' spatiotemporal pattern extraction abilities, enabling the successful implementation of a real-time population-based MPC in systems with many controlled variables. In particular, we propose a data-driven intelligent controller that leverages NN-based digital twins for hypothesis testing. Initially, a diverse set of control laws is generated using genetic programming with the digital twin of the system, facilitating a robust response to unknown disturbances. During inference, the trained digital twin is utilized to virtually test alternative control actions for a multi-objective optimization task associated with each control action. Subsequently, the best policy is applied to the system. To evaluate the proposed intelligent control pipeline, experiments are conducted on a multi-mode heat transfer test rig.