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Abstract Physics-informed machine learning bridges the gap between the high fidelity of mechanistic models and the adaptive insights of artificial intelligence. In chemical reaction network modeling, this synergy proves valuable, addressing the high computational costs of detailed mechanistic models while leveraging the predictive power of machine learning. This study applies this fusion to the biomedical challenge of A$$\beta$$fibril aggregation, a key factor in Alzheimer’s disease. Central to the research is the introduction of an automatic reaction order model reduction framework, designed to optimize reduced-order kinetic models. This framework represents a shift in model construction, automatically determining the appropriate level of detail for reaction network modeling. The proposed approach significantly improves simulation efficiency and accuracy, particularly in systems like A$$\beta$$aggregation, where precise modeling of nucleation and growth kinetics can reveal potential therapeutic targets. Additionally, the automatic model reduction technique has the potential to generalize to other network models. The methodology offers a scalable and adaptable tool for applications beyond biomedical research. Its ability to dynamically adjust model complexity based on system-specific needs ensures that models remain both computationally feasible and scientifically relevant, accommodating new data and evolving understandings of complex phenomena. 

The rapid growth of diverse -omics datasets has made multiomics data integration crucial in cancer research. This study adapts the expectation–maximization routine for the joint latent variable modeling of multiomics patient profiles. By combining this approach with traditional biological feature selection methods, this study optimizes latent distribution, enabling efficient patient clustering from well-studied cancer types with reduced computational expense. The proposed optimization subroutines enhance survival analysis and improve runtime performance. This article presents a framework for distinguishing cancer subtypes and identifying potential biomarkers for breast cancer. Key insights into individual subtype expression and function were obtained through differentially expressed gene analysis and pathway enrichment for BRCA patients. The analysis compared 302 tumor samples to 113 normal samples across 60,660 genes. The highly upregulated gene COL10A1, promoting breast cancer progression and poor prognosis, and the consistently downregulated gene CDG300LG, linked to brain metastatic cancer, were identified. Pathway enrichment analysis revealed similarities in cellular matrix organization pathways across subtypes, with notable differences in functions like cell proliferation regulation and endocytosis by host cells. GO Semantic Similarity analysis quantified gene relationships in each subtype, identifying potential biomarkers like MATN2, similar to COL10A1. These insights suggest deeper relationships within clusters and highlight personalized treatment potential based on subtypes. 

In this paper, we discuss some well-known experimental observations on self-organization in dissipative systems. The examples range from pure fluid flow, pattern selection in fluid–solid systems to chemical-reaction-induced flocking and aggregation in fluid systems. In each case, self-organization can be seen to be a function of a persistent internal gradient. One goal of this article is to hint at a common theory to explain such phenomena, which often takes the form of the extremum of some thermodynamic quantity, for instance the rate of entropy production. Such variational theories are not new; they have been in existence for decades and gained popularity through the Nobel Prize-winning work of theorists such as Lars Onsager and Ilya Prigogine. The arguments have evolved since then to include systems of higher complexity and for nonlinear systems, though a comprehensive theory remains elusive. The overall attempt is to bring out examples from physics, chemistry, engineering, and biology that reveal deep connections between variational principles in physics and biological, or living systems. There is sufficient evidence to at least raise suspicion that there exists an organization principle common to both living and non-living systems, which deserves deep attention.