Dehraj, SanaullahUmar, MuhammadSalahshour, SoheilBano, AmbreenBanaras, Muhammad RehanAli, Mohamed2026-04-212026-04-2120261868-64781868-648610.1007/s12530-026-09806-02-s2.0-105033452565https://hdl.handle.net/123456789/8966https://doi.org/10.1007/s12530-026-09806-0The present investigations provide the solutions to the human liver system by a neuro computing stochastic structure. The dynamics of the human liver system have two classes: blood and liver. The tests of optimization are performed by the Levenberg-Marquardt backpropagation neural network (LMBNN) structure using a single hidden layer, thirteen neurons and a log-sigmoid activation function for solving the human liver model. The reference database results are obtained through the Adam solver, which is used to lessen the mean square error in the sense of training, authorization, and testing. The correctness of the designed LMBNN procedure is presented through the assessment of reference and accomplished results, and best authentication achieved as 10(- 11), 10(- 13), and 10(- 14), while the negligible absolute errors as 10(- 06) to 10(- 09) provide the authenticity of the designed LMBNN. The accuracy of the solver using different statistical analysis including regression performances 1, state transition, and error histogram is also presented.eninfo:eu-repo/semantics/closedAccessNeural StructureNumerical ResultsHuman LiverLevenberg-marquardtComparisonArticle