The present study implements the incompressible smoothed particle hydrodynamics (ISPH) method with an artificial neural network (ANN) to simulate the impacts of Cattaneo-Christov heat flux on the double diffusion of a nanofluid inside a square cavity. The cavity contains a rotated wavy circular cylinder and four fins fixed on its borders. The rotational motion of an inner wavy cylinder interacting with a nanofluid flow is handled by the ISPH method. An adiabatic thermal/solutal condition is applied for the embedded wavy cylinder and the plane cavity's walls. The left wall is a source of the temperature and concentration, $T_h\mathrm{\&}{C}_h$, and the right wall with the four fins is maintained at a low temperature/concentration, $T_c\mathrm{\&}{C}_c$. The pertinent parameters are the Cattaneo-Christov heat flux parameter $\left({0\le \delta }_c\le 0.001\right)$, the Dufour number $\left(0\le Du\le 2\right)$, the nanoparticle parameter $\left(0\le \varphi \le 0.1\right)$, the Soret number $\left(0\le Sr\le 2\right)$, the Hartmann number $\left(0\le Ha\le 80\right)$, the Rayleigh number $\left({10}^3\le Ra\le {10}^5\right)$, Fin's length $\left({0.05\le L}_{Fin}\le 0.2\right)$, and the radius of a wavy circular cylinder $\left(0.05\le R_{Cyld}\le 0.3\right)$. The results revealed that the maximum of a velocity field is reduced by $48.65\mathrm{\%}$ as the $L_{Fin}$ boosts from $0.05$ to $0.2$, and by $55.42\mathrm{\%}$ according to an increase in the $R_{Cyld}$ from $0.05$ to $0.3$. Adding a greater concentration of nanoparticles until 10% increases the viscosity of a nanofluid, which declines the velocity field by $36.52\mathrm{\%}.$ The radius of a wavy circular cylinder and the length of four fins have significant roles in changing the strength of the temperature, the concentration, and the velocity field. Based on the available results of the ISPH method for $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$, an ANN model is developed to predict these values. The ideal agreement between the prediction and target values of $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ indicates that the developed ANN model can forecast the $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ values with a remarkable accuracy.