# Process-Informed Forecasting of Complex Thermal Dynamics in Pharmaceutical Manufacturing

arXiv: https://arxiv.org/abs/2509.20349 · HTML: https://mlsanity.com/paper/2509.20349/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [Residual-based attention in physics-informed neural networks](https://mlsanity.com/paper/2307.00379/) (2023)
- [Long Expressive Memory for Sequence Modeling](https://mlsanity.com/paper/2110.04744/) (2021)
- [TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers](https://mlsanity.com/paper/2307.02588/) (2023)
- [Neural oscillators for generalization of physics-informed machine learning](https://mlsanity.com/paper/2308.08989/) (2023)
- [Kolmogorov-Arnold Networks in Low-Data Regimes: A Comparative Study with Multilayer Perceptrons](https://mlsanity.com/paper/2409.10463/) (2024)
- [Learning via Long Short-Term Memory (LSTM) network for predicting strains in Railway Bridge members under train induced vibration](https://mlsanity.com/paper/2111.06259/) (2021)

## Abstract (arXiv)

Accurate time-series forecasting for complex physical systems is the backbone of modern industrial monitoring and control, yet deep learning models often lack the physical consistency required in regulated environments.To bridge this gap, we introduce Process-Informed Forecasting (PIF) models for temperature in pharmaceutical lyophilization, embedding deterministic production recipes as macro-structural priors. We investigate classical methods (e.g., Autoregressive Integrated Moving Average (ARIMA) model) and 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 to a new process. Our results show that PIF models outperform their data-driven counterparts in terms of accuracy, physical plausibility and noise resilience, offering a scalable framework for reliable and generalizable forecasting solutions in critical manufacturing.