Knowledge-embedded machine learning for production optimization on logistical delivery grids

Abstract Measurement uncertainty is often treated as noise to be reduced, but in reality, it reflects a mismatch between point-based observations and the underlying stochastic nature of physical processes. In scenarios involving both regression targets and classification-based thresholds, this discrepancy can be systematically exploited for improved optimization. We propose a novel training approach based on a compound loss function that integrates two inputs describing the same target: a metric signal (e.g., a physical measurement) and a categorical estimate (e.g., derived from expert judgment, statistical aggregation, or repeated sampling). This dual-input strategy reflects how individual noisy observations differ from their expected behavior over time and uses this difference to optimize learning under aleatoric uncertainty. The approach is model-agnostic, scalable to multiple targets, and allows for tuning prior knowledge contributions via a weighting parameter. Using synthetic data derived from opto-semiconductor measurements, we demonstrate a +17.78% improvement in delivery conformity under realistic constraints, with only a marginal increase in normalized regression error (ΔMAE = +0.0073). These results highlight the method’s practical applicability and its scalability to complex, multi-target optimization scenarios.