Process-Informed Forecasting of Complex Thermal Dynamics in Pharmaceutical Manufacturing

Abstract

Accurate time-series forecasting for complex physical systems is the backbone of modern industrial monitoring and control. While deep learning models excel at capturing complex dynamics, currently, their deployment is limited due to physical inconsistency and robustness, hence constraining their reliability in regulated environments. We introduce process-informed forecasting (PIF) models for temperature in pharmaceutical lyophilization. We investigate a wide range of models, from classical ones such as Autoregressive Integrated Moving Average Model (ARIMA) and Exponential Smoothing Model (ETS), to modern deep learning architectures, including Kolmogorov-Arnold Networks (KANs). We compare three different loss function formulations that integrate a process-informed trajectory prior: a fixed-weight loss, a dynamic uncertainty-based loss, and a Residual-Based Attention (RBA) mechanism. We evaluate all models not only for accuracy and physical consistency but also for robustness to sensor noise. Furthermore, we test the practical generalizability of the best model in a transfer learning scenario on a new process. Our results show that PIF models outperform their data-driven counterparts in terms of accuracy, physical plausibility and noise resilience. This work provides a roadmap for developing reliable and generalizable forecasting solutions for critical applications in the pharmaceutical manufacturing landscape.