Machine learning approach for predicting heat and mass transfer in Maxwell–Sutterby fluid flow over a Riga plate geometry via Levenberg–Marquardt backpropagation neural network algorithm: influence of joule heating and activation energy

• Coupled Maxwell–Sutterby nanofluid with activation energy and motile microorganisms over a Riga plate has not been previously investigated. • Incorporation of variable thermal conductivity and Nield boundary conditions within this framework provides new insights into heat and mass transport mechanisms. • Artificial Neural Network (ANN) modelling integrated with bvp5c solutions is applied for predictive analysis and validation, showing strong agreement and offering a computationally efficient alternative. • The results reveal new correlations between Hartmann number, thermal radiation, and thermophoresis effects on velocity, temperature, concentration, and microorganism density distributions. • The study also reports, for the first time, that increasing activation energy reduces reactive species concentration while motile microbe dynamics stabilize the flow, highlighting combined effects not addressed in earlier works. Activation energy is vital in chemical kinetics, influencing reaction rates and aiding in understanding and optimizing various industrial processes. This research aims to investigate the significance of activation energy on magnetized flow of Maxwell–Sutterby fluid bounded by Riga plate in the presence of motile microbes. For the inspiration of problem, the influence of variable thermal conductivity along with Nield boundary conditions are deliberated with ANNs modelling. The theory of heat transfer with joule heating and thermal radiation is measured. The governing PDEs of Maxwell–Sutterby fluid is transformed into nonlinear ODEs via similarity platform. The couple of obtained ODEs is solved via bvp5c in MATLAB then ANN is applied with Levenberg Marquardt training approach to them. The back propagation neural network is used to forecast the intended results. Graphical and tabulated outcomes are carryout for involved profiles such that fluids velocity f ′ , temperature θ , concentration ϕ and microbes χ over prominent parameters of interests. Further the graphs of physical quantities are also plotted. It is noticed that the skin friction factor C f falls as the Hartmann number H rises, indicating a decline in surface shear stress. Conversely, the Nusselt number Nu boosts for developed values of H , indicating improved heat transfer at the surface. Furthermore, a rise in the thermophoresis parameter Nt improves the volumetric concentration distribution.