Time series (TS) data are ubiquitous across various application areas, rendering time series forecasting (TSF) a fundamental task. With the astounding advances in large language models (LLMs), a variety of methods have been developed to adapt LLMs for time series forecasting. Despite unlocking the potential of LLMs in comprehending TS data, existing methods are inherently constrained by their shallow integration of TS information, wherein LLMs typically access TS representations at shallow layers, primarily at the input layer. This causes the influence of TS representations to progressively fade in deeper layers and eventually leads to ineffective adaptation between textual embeddings and TS representations. In this paper, we propose the Multi-layer Steerable Embedding Fusion (MSEF), a novel framework that enables LLMs to directly access time series patterns at all depths, thereby mitigating the progressive loss of TS information in deeper layers. Specifically, MSEF leverages off-the-shelf time series foundation models to extract semantically rich embeddings, which are fused with intermediate text representations across LLM layers via layer-specific steering vectors. These steering vectors are designed to continuously optimize the alignment between time series and textual modalities and facilitate a layer-specific adaptation mechanism that ensures efficient few-shot learning capabilities. Experimental results on seven benchmarks demonstrate significant performance improvements by MSEF compared with baselines, with an average reduction of 31.8% in terms of MSE. The code is available at https://github.com/One1sAll/MSEF.

The steel industry has received serious attention under the background of carbon neutralization and carbon peaking. However, the traditional end-to-end energy consumption (EC) prediction method does not consider the effects of multi-step rolling, multi-time series, and error accumulation. To this end, a series-concatenation model based on a two-stage hybrid network is proposed to achieve EC high-precision prediction in multi-step continuous rolling. Specifically. First, this paper analyzed the mechanism between rolling EC and multiple variables. Second, a two-stage hybrid network with a deep neural network block, convolutional neural network block, long short-term memory block, and SoftBoost block (DCLS-Net) is established for EC prediction of single-step rolling. SoftBoost block is a double-layer structure method proposed in this paper for multi-block precision improvement based on two kinds of boosting strategies. Last, according to the error mechanism and multi-time series characteristics in the multi-step rolling, a series-concatenation EC prediction model is designed to suppress errors and achieve high-precision prediction. The experimental results show that the SoftBoost can effectively improve prediction performance. And the prediction precision of the two-stage DCLS-Net for single-step rolling is improved by 9.43% on average compared with the end-to-end machine learning algorithm. Furthermore, the precision of the series-concatenation model for multi-step rolling is improved by 4.96% compared with the traditional series model, which can satisfy the requirements of high accuracy and positive error in strip rolling production.Note to Practitioners—The inspiration for this paper mainly comes from the multi-objective process planning problem in the hot multi-step continuous roughing process, especially the energy consumption target. This method is also applicable to other variable prediction problems in the continuous multi-step process industry. The common method of energy consumption prediction is end-to-end machine learning. However, the characteristics of multi-step rolling and multi-time series, as well as the influence of intermediate process variables on the results, are not considered, which makes the precision and reliability of prediction unable to satisfy the requirements of industrial production. In this paper, the series-concatenation model structure is adopted to realize the high-precision energy consumption prediction and error suppression of multi-step rolling of strip steel. Such research is helpful for engineers to understand the energy consumption mechanism of strip rolling. It provides guidance for multi-objective roughing process planning. In future research, we will study the influence of more process variables on energy consumption.

The steel industry is the key industry of energy consumption. The optimization of rolling process parameters is an effective measure to reduce and optimize energy consumption. Accurate energy consumption prediction has an indispensable guiding function in the planning of process parameters. However, the traditional energy consumption prediction and machine learning methods have been unable to fit the needs of high precision and reliability. Taking the horizontal roughing process (HRP) of hot rolling process as the research object, this paper mainly introduces an energy consumption prediction mechanism model (ECPMM) based on a roller adaptive wear strategy by analyzing the strip forming mechanism and rolling process. Then, two directions adaptive differential evolution (TDADE) algorithm is proposed based on a novel adaptive strategy. This algorithm has better convergence speed and global optimization ability than other optimization algorithms in the parameter optimization of ECPMM. We carried out comparative experiments on five machine learning algorithms. The results show that the ECPMM optimized by TDADE is superior to the five machine learning algorithms in prediction accuracy and stability. Finally, we conducted ablation experiments on the energy consumption characteristics of the HRP process, which turns out that using a smaller reduction and roller radius can reduce energy consumption. Summarizing the above experimental results suggests that the ECPMM has high accuracy and robustness, and satisfies the requirements of practical application. Note to Practitioners—It is necessary to carry out the deep analysis and research of energy consumption prediction involved in the process planning of strip hot rolling, the inspiration of this article is stem from this point. The commonly used energy consumption prediction methods include mechanism modeling and machine learning, but both have disadvantages, like low prediction accuracy and black box, which must have to be performed to solve by adapting the production demand of high reliability. In this paper, the combination of the mechanism model and data-driven method is used to realize the accurate prediction of energy consumption and improve the reliability of the model. To the best of our knowledge, this is the first paper about the research on energy consumption prediction of hot rolling process based on mechanism model and data-driven, especially in data size, time granularity, algorithm design, and prediction performance. Such research is helpful to guide engineers to design rolling energy consumption. We will dive a bit deeper into learning the energy consumption and process parameters during the rolling process in future studies.

Due to the massive uncertain disturbances in water distribution systems (WDSs), it is rather challenging to construct robust macroscopic pressure models. In this article, we propose the CritiCoder, an end-to-end uncertain regression neural network, to build macroscopic pressure models in WDSs and estimate the distribution of uncertain disturbances. By separating the normal regression process into two parts, the CritiCoder decomposes the output into two parts brought by observable and unobservable variates separately. Two subnetworks, Coder and Critic, make up of the CritiCoder. Through the reconstruction of data flow, the Coder is expected to approximate ideal outputs from observable variates. Meanwhile, the loss function of the Critic is redesigned to consider the effectiveness of uncertain disturbances in output brought by unobservable variates. Experiments on a practical application of WDSs in a Chinese mega-city show superior performance of CritiCoder. Especially for pressure-monitoring nodes more severely impacted by disturbances, the performance decline of the CritiCoder is less compared with other baseline methods.

The policy gradient adaptive dynamic programming (PGADP) technique has gained recognition as an effective approach for optimizing the performance of nonlinear systems. Nonetheless, existing PGADP algorithms often demand a substantial volume of expensive or potentially risky interaction data with the system. Moreover, the utilization of neural networks in these algorithms can result in suboptimal learning efficiency and unstable training procedures. To address these challenges, a novel algorithm, referred to as OptNet-PGADP, has been introduced. This algorithm integrates an initially tailored control policy based on OptNet to tackle the optimization of control problems in discrete-time nonlinear systems. The OptNet-PGADP algorithm operates through a two-step process. Initially, the input–output trajectory of the system is computed using the nonlinear model predictive control (NMPC) method. Subsequently, an initial admissible control policy is acquired through OptNet. This policy is iteratively enhanced using the PGADP algorithm to attain the optimal controller. The resulting closed-loop control policy can be readily deployed in real-time applications. The implementation of the algorithm employs OptNet for the actor network and integrates an experience replay mechanism to bolster the controller’s learning efficiency. Furthermore, a convergence and optimality analysis of the algorithm is included. Simulation and experimental results conducted on two nonlinear systems conclusively demonstrate that the approach outperforms traditional PGADP and NMPC algorithms. These findings underscore the efficacy of OptNet-PGADP in mitigating the constraints of current methods and achieving superior control performance for nonlinear systems.

Policy gradient adaptive dynamic programming (PGADP) is a recently acclaimed control technique for the optimal control design of nonlinear systems. Nevertheless, it demands a substantial amount of interaction data with the controlled system, which can prove costly or perilous in certain scenarios. This article introduces a parallel cross entropy optimization method-based PGADP (PCEOM-PGADP) algorithm, with the objective of devising an optimal tracking controller for discrete-time nonlinear systems. The tracking problem is transformed into a regulation problem by constructing a tracking error system. Furthermore, the implementation of the proposed algorithm employs an actor–critic structure, where the actor network represents the control policy and the critic network assesses its performance. Through the iterative interaction, the optimal policy is ultimately derived. The approach also leverages the parallel cross entropy optimization method (PCEOM) to acquire a reasonable initial control policy for PGADP, thereby accelerating the efficiency of the learning process. Convergence analysis of the algorithm is conducted by demonstrating that the generated$Q$function constitutes a monotonically nonincreasing sequence. Finally, the effectiveness of the proposed PCEOM-PGADP algorithm is verified through simulation on a complex automated driving tracking system.

Extensive research has been dedicated to reinforcement learning (RL) for acquiring proficient optimal controllers through interactions with the environment. However, real-world demands, including enhanced safety performance, introduce considerable challenges to the present design of optimal controllers rooted in RL algorithms. A novel approach is introduced in this article for designing RL-based optimal controllers, employing a control barrier function (CBF) alongside a nonquadratic loss function related to the control signal. The aim is to enable the agent to learn the optimal controller in a secure and efficient manner. To tackle the instability issue in neural network training inherent to traditional RL-based controller design processes, the nonlinear model predictive control (NMPC) technique is employed for initializing the controller network’s weights. A formal demonstration of the method’s optimality is presented. Numerical simulations validate the proposed approach, illustrating its capacity to effectively learn the optimal controller while adhering to the input and state constraints of the system.