Physics-informed machine learning (PIML) refers to the emerging area of extracting physically relevant solutions to complex multiscale modeling problems lacking sufficient quantity and veracity of data with learning models informed by physically relevant prior information. This work discusses the recent critical advancements in the PIML domain. Novel methods and applications of domain decomposition in physics-informed neural networks (PINNs) in particular are highlighted. Additionally, we explore recent works toward utilizing neural operator learning to intuit relationships in physics systems traditionally modeled by sets of complex governing equations and solved with expensive differentiation techniques. Finally, expansive applications of traditional physics-informed machine learning and potential limitations are discussed. In addition to summarizing recent work, we propose a novel taxonomic structure to catalog physics-informed machine learning based on how the physics-information is derived and injected into the machine learning process. The taxonomy assumes the explicit objectives of facilitating interdisciplinary collaboration in methodology, thereby promoting a wider characterization of what types of physics problems are served by the physics-informed learning machines and assisting in identifying suitable targets for future work. To summarize, the major twofold goal of this work is to summarize recent advancements and introduce a taxonomic catalog for applications of physics-informed machine learning.

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.

SARS-CoV-2 continues to upend human life by posing novel threats related to disease spread and mutations. Current models for the disease burden of SARS-CoV-2 consider the aggregate nature of the virus without differentiating between the potency of its multiple strains. Hence, there is a need to create a fundamental modeling framework for multi-strain viruses that considers the competing viral pathogenic pathways. Alongside the consideration that other viral pathogens may coexist, there is also a need for a generalizable modeling framework to account for multiple epidemics (i.e., multi-demics) scenarios, such as influenza and COVID-19 occurring simultaneously. We present a fundamental network thermodynamics approach for assessing, determining, and predicting viral outbreak severity, which extends well-known standard epidemiological models. In particular, we use historical data from New York City’s 2011–2019 influenza seasons and SARS-CoV-2 spread to identify the model parameters. In our model-based analysis, we employ a standard susceptible–infected–recovered (SIR) model with pertinent generalizations to account for multi-strain and multi-demics scenarios. We show that the reaction affinities underpinning the formation processes of our model can be used to categorize the severity of infectious or deceased populations. The spontaneity of occurrence captured by the change in Gibbs free energy of reaction ($∆G$) in the system suggests the stability of forward occurring population transfers. The magnitude of $∆G$ is used to examine past influenza outbreaks and infer epidemiological factors, such as mortality and case burden. This method can be extrapolated for wide-ranging utility in computational epidemiology. The risk of overlapping multi-demics seasons between influenza and SARS-CoV-2 will persist as a significant threat in forthcoming years. Further, the possibility of mutating strains requires novel ways of analyzing the network of competing infection pathways. The approach outlined in this study allows for the identification of new stable strains and the potential increase in disease burden from a complex systems perspective, thereby allowing for a potential response to the significant question: are the effects of a multi-demic greater than the sum of its individual viral epidemics?

The rapid growth of diverse $\text{-}\mathrm{omics}$ 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.

Emerging diseases—and none as recently or devastatingly impactful toward humans as COVID-19—pose an immense challenge to researchers concerned with infectious disease. This study is tasked with expanding the computational probe of treatment regimes in a differential equations-based model of the SARS-CoV-2 host–virus interaction. Parameters within the model are tweaked to simulate dose specifications. Further, parametric variations are introduced in a timed manner to infer the importance of dose timing. Arming in silico testing, and eventually, clinical testing, with abundant information on simulated therapeutic regimes is the overall contribution of this pharmacodynamic model; thus, a wide range of dose and timing combinations are examined. Therapeutic interventions that block viral replication inhibit viral entry into host cells, and vaccination-induced antibodies are all studied alone and in combination. Especially during early detection, exhaustive parameter sweeps of well-suited within-host models are often the first step in the clinical response to a novel disease.