Accelerating Industrial Carbon Footprint Reduction: AI-Enhanced Numerical Optimal Control of Complex Manufacturing Processes Using Hybrid PDE-ABM Models

Vincent Major Bulinda
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Vincent Major Bulinda: Department of Mathematics & Actuarial Science, Kisii University, KENYA

International Journal of Research and Innovation in Applied Science, 2025, vol. 10, issue 7, 473-479

Abstract: In order to balance carbon emissions and thermal efficiency through coupled thermal dynamics and machine scheduling, this study proposes a hybrid PDE-ABM model that incorporates AI. Partial Differential Equations (PDEs) model continuous physical processes like heat transfer, while Agent-Based Models (ABMs) capture discrete operational decisions such as scheduling. The model’s simulations combine an ABM for machine activity with a PDE-based heat equation to produce actual data that is plotted. When compared to dynamic synthetic profiles, the carbon emission rate shows suboptimal reduction due to step-like patterns that are constrained by a constant heuristic control. Weak hotspots in the temperature field indicate inadequate heating in comparison to synthetic Gaussians, which could affect operational feasibility. Thermal feedback sensitivity is reflected in the lower number of active machines compared to synthetic predictions when machine activity is driven by temperature thresholds. Contrary to synthetic assumptions, heat sources have sparse, frequently absent inputs, and machine temperatures stay below operating thresholds, which restricts output. The necessity of dynamic optimization is emphasized by constant control inputs. These findings confirm that the model can accurately represent PDE-ABM interactions, but they also highlight the shortcomings of the heuristic control and the necessity of sophisticated optimization to achieve long-term, effective furnace operations.

Date: 2025
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