To improve the thermal management systems in industrial operations, there is a need for the prediction and complexity of advanced fluid motion across various physical conditions on different geometries. Further, ternary nanofluid flow across curved Riga surfaces plays a significant role in thermal management systems, chemical industries, thermal management systems, biomedical, environmental engineering, and more. Based on the above importance the current study focuses artificial neural network (ANN) model on the ternary nanofluid flow over a curved Riga surface in the presence of chemical reaction and activation energy. Proper assumptions and boundary layer approximation were used to develop the model. Using appropriate similarity variables, the governing equations are further simplified to ordinary differential equations (ODEs). Runge Kutta Fehlberg's 4th-5th order and shooting process are applied to solve the simplified equations. The primary objective is to improve the construction and optimization of thermal administration systems and other manufacturing procedures by gaining a deeper knowledge of the fluid motion and characteristics of heat transfer involved. Graphs are used to provide additional context for the important dimensionless constraints. The obtained data was utilized to train the ANN model, which was then verified towards numerical values of important engineering coefficients. The results reveal that the addition of solid volume fraction will enhance the thermal profile while declining the concentration profile. The reaction rate parameter will decline the concentration, and a reverse trend is seen for the activation energy parameter. The constructed model exhibits an outstanding degree of precision throughout the procedure, spanning all phases of the research.