Food manufacturing faces challenges in balancing efficiency, energy use, and quality. This paper presents a Hybrid Digital Twin Architecture (HDTA). It combines simulation, constraint programming, and Industrial IoT into a closed-loop system. The architecture has three layers: simulation for planning, optimization for scheduling, and an edge layer for control. We validated this using a bakery model with 10 products. The results show a 24.4% reduction in production time and 23% energy savings. Simulation results show complete elimination of quality time-window violations (0.0% vs. 13.3% baseline, p < 0.001). The system achieved a 2.4-month return on investment. This work demonstrates how combining these technologies can improve process industries.

In this paper, a digital twin of the network of heating systems for smart cities is developed using the example of the city of Almaty. The study used machine learning algorithms to estimate future thermal energy consumption and develop thermodynamic formulas. This work offers a thorough and in-depth analysis of thermal energy consumption. In addition, the paper identifies the relationship between thermal energy consumption and ambient temperature, and wind uncertainty in certain urban areas using machine learning methods to predict thermal energy consumption. Using both training and regression models, this interdependence is revealed. The obtained forecasts provide useful information for studying the structure of heat consumption in Almaty and reducing heat losses by reducing overheating in the zones of heating networks. In addition, the study analyzes high-resolution spatial data collected from 385 homes and 62 heat transfer circuits located throughout the city during the heating season. The study examines the degree of relationship between the ambient temperature and the amount of heat energy used in the areas of Astana. A minor impact of wind speed is also estimated. These discoveries allow us to use machine learning algorithms to find the location of hot spots and inefficient zones with high losses.

Currently, the theory and methods of machine learning (ML) are rapidly developing and are increasingly used in various fields of science and technology, in particular in manufacturing, education and medicine. Weakly supervised learning is a subset of machine learning research that aims to develop models and methods for analyzing various types of information. When formulating a weakly supervised learning problem, it is assumed that some objects in the model are not defined correctly. This inaccuracy can be understood in different ways. Weakly supervised learning is a type of machine learning method in which a model is trained using incomplete, inaccurate, or imprecise observation signals rather than using fully validated data. Weakly supervised learning often occurs in real-world problems for various reasons. This may be due to the high cost of the data labeling process, low sensor accuracy, lack of expert experience, or human error. For example, labeling of poor control is carried out in cases obtained by crowdsourcing methods: for each object there is a set of different assessments, the quality of which depends on the skill of the performers. Another example is the problem of object detection in an image. Boundary lines are a common way to indicate the location and size of objects detected in an image in object detection tasks. The article presents an algorithm for solving a multi-objective weakly supervised regression problem using the Wasserstein metric, various regularizations and a co-association matrix as a similarity matrix. The work also improved the algorithm for calculating the weighted average co-association matrix. We compare the proposed algorithm with existing supervised learning and unsupervised learning algorithms on synthetic and real data.

Industrial energy consumption in shift-based manufacturing exhibits pronounced temporal asymmetry—here defined as direction-dependent conditional dynamics in which the transition from production to shutdown states follows a systematically different temporal trajectory than the reverse transition. At the facility studied, this asymmetry also manifests in the marginal distribution of hourly consumption values: pooling all 4724 observations yields a bimodal, right-skewed histogram (skewness ≈ −0.4) comprising two sub-populations corresponding to production hours (14–19 kWh/h) and shutdown hours (0–2 kWh/h). Although individual hourly observations are serially dependent and therefore not i.i.d., the marginal distributional shape is consequential because ARIMA-class models assume approximately Gaussian innovations, and residuals from models fit to this bimodal series inherit its non-Gaussianity. More fundamentally, the conditional distribution P(E_t|E_{t − 1}, …) is direction-dependent: the production-to-shutdown transition is abrupt (1–2 h, 18:00–20:00), while the shutdown-to-production ramp is slower and more variable (2–4 h, 05:00–07:00). Symmetric ARMA models, applying identical autoregressive coefficients regardless of transition direction, cannot represent this directional asymmetry, rendering their assumptions and associated error metrics structurally unreliable for this class of data. This paper addresses this asymmetry directly by presenting and evaluating two hybrid forecasting architectures—Prophet+LSTM and SARIMA+LSTM—for 24 h-ahead energy prediction at an industrial bread factory in Kazakhstan, instrumented with 15 IoT energy meters. The two-stage design exploits the complementary asymmetry-handling properties of each component: the statistical model (Prophet or SARIMA) captures deterministic seasonal structure, while the LSTM corrects asymmetric residuals that the statistical model systematically misrepresents. In a rigorous 14-day holdout evaluation, Prophet+LSTM achieves an MAE of 3.39 kWh—outperforming the Seasonal Naïve baseline by 12.3% and reducing Prophet-alone error by 32.7%—with statistical significance at the 10% level confirmed via Diebold–Mariano testing (DM = +1.747, p = 0.081). The LSTM residual correction reduces Prophet’s systematic negative bias by 69% (from −3.60 to −1.13 kWh), as confirmed by ablation testing. In eight weeks of production operation with incremental retraining, MAE improved 35% (7.02 → 4.58 kWh). These results demonstrate that explicitly modelling temporal asymmetry through hybrid statistical-neural architectures substantially improves industrial energy forecasting accuracy.