Deep-Learning Augmented PDE Models for Cellular Metabolic Regulation: An Integrative Biochemistry–AI Approach

Abstract

By combining basic biochemical laws with advanced AI-based learning, PDE models with deep learning have become an effective way to describe the multiscale dynamics of cellular metabolic regulation. The primary aim of this study is to develop an AI-enhanced biochemistry model capable of identifying metabolic phenomena that are either obscured or overlooked by conventional PDE models. The method has two parts for preprocessing: one that utilises deep learning to get features and another that employs statistical cleaning, normalisation, and stratification. Then, a GLM core that has been improved using Mantel-Haenszel stratified analysis to account for confounding effects is used to build the model. A hybrid deep learning architecture and a fusion module based on transformers are utilised to combine distinct biological inputs and learn patterns based on both partial differential equations (PDEs) and data. The results demonstrate a big improvement in computational efficiency, with a runtime that is about 26.7% faster, a cost that is about 18% cheaper, and a predictive performance that is around 0.91 AUC and 0.88 F1-score. The log-binomial model has the greatest accuracy (93%). The results indicate that PDE frameworks using deep learning provide a high-performance, interpretable, and scalable method for characterising metabolic rewiring, which is advantageous for metabolic engineering and precision biology.