Artificial Intelligence and Differential Equations in Postmortem Interval Estimation: A Critical Review of Cadaver Cooling Models and their Applications in Criminal Investigation

This review examines the relationship between cadaver cooling, differential equations and artificial intelligence in postmortem interval estimation, distinguishing computational plausibility from forensic validation. A critical narrative review of 60 references combined documentary screening, individual bibliographic identity checks and examination of available abstracts or full texts. The synthesis distinguished controlled experiments, human observations and computational foundations. Thermal models make mechanisms explicit, but their inversion depends on partly unknown initial and environmental conditions. Machine learning incorporates metabolomic, molecular and imaging information; heterogeneous performance measures do not establish overall superiority. Surrogate-based optimization provides a documented integration of physical simulation and computation in human cadavers, although validation remains limited. Physics-informed neural networks offer tools for inverse problems; computational effectiveness alone does not establish forensic usefulness. Translation into criminal investigation requires a defined application domain, separation of decedents between training and evaluation, assessment of calibration and uncertainty, and external validation. A model should be judged by the reliability of its inferences under documented conditions as well as its predictive fit.