Modeling Batch Crystallization under Uncertainty Using Physics-informed Machine Learning

2026-02-06

AI Summary

This work addresses the challenges of uncertainty in batch crystallization modeling arising from measurement noise, solubility model bias, and sparse sampling. To this end, the authors propose a Physics-Informed Recurrent Neural Network (PIRNN), which, for the first time, integrates a physics-informed learning framework into uncertain crystallization processes. The method embeds the population balance equation as a physical constraint and employs adaptive-weight physics regularization to jointly learn from data and governing equations. Even under conditions of low sampling rates, model mismatch, and systematic solubility deviations, PIRNN accurately recovers kinetic parameters while preserving physical consistency. Experimental results demonstrate that, in the presence of systematic errors in the solubility model, PIRNN improves prediction accuracy by over an order of magnitude compared to purely data-driven approaches, substantially enhancing model robustness, generalizability, and industrial applicability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

The development of robust and reliable modeling approaches for crystallization processes is often challenging because of non-idealities in real data arising from various sources of uncertainty. This study investigated the effectiveness of physics-informed recurrent neural networks (PIRNNs) that integrate the mechanistic population balance model with recurrent neural networks under the presence of systematic and model uncertainties. Such uncertainties are represented by using synthetic data containing controlled noise, solubility shift, and limited sampling. The research demonstrates that PIRNNs achieve strong generalization and physical consistency, maintain stable learning behavior, and accurately recover kinetic parameters despite significant stochastic variations in the training data. In the case of systematic errors in the solubility model, the inclusion of physics regularization improved the test performance by more than an order of magnitude compared to purely data-driven models, whereas excessive weighting of physics increased error arising due to the model mismatch. The results also show that PIRNNs are able to recover model parameters and replicate crystallization dynamics even in the limit of very low sampling resolution. These findings validate the robustness of physics-informed machine learning in handling data imperfections and incomplete domain knowledge, providing a potential pathway toward reliable and practical hybrid modeling of crystallization dynamics and industrial process monitoring and control.

Problem

• batch crystallization
• uncertainty
• physics-informed machine learning
• modeling
• data imperfections

Innovation

• physics-informed machine learning
• recurrent neural networks
• population balance model
• crystallization modeling
• uncertainty quantification