The aim of the current research is to compare the surface roughness models based on the Box–Behnken Design and Levenberg–Marquardt Algorithm-based artificial neural networks. For prediction of the surface roughness of magnetic abrasive flow machining (MAFM) finished rare earth oxides (REOs) aluminium composites, Box–Behnken Design models were developed using three-level factorial design as magnetic flux density, number of cycles and extrusion pressure as process parameters. The artificial neural networks predictive models of surface roughness were developed using feed forward back propagation network procedures called the Levenberg-Marquardt Algorithm. Also, an attempt has been made to compare the Levenberg–Marquardt Algorithm-based artificial neural networks and Box–Behnken Design for the modeling of surface roughness results. The value of coefficient of determination for the Box–Behnken Design model is found to be high ( R2 = 0.9737), which is an indication of good fit for the model with high significance. The percentage error for the Box–Behnken Design model is observed to be more as compared to the Levenberg–Marquardt Algorithm-based artificial neural networks model. The comparison evidently indicates that the prediction capabilities of trained artificial neural networks models are far better than the Box–Behnken Design models. Further, specimens were examined using atomic force microscopy for three-dimensional surface profiles.

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