Asad Ullah ^1* Yao Hongxing ¹ Farid Ullah ² Haifa Alqahtani ³ Emad A. Ismail ⁴ Fuad Awwad ⁴ Abeer A. Shaaban ⁵

• ¹ Jiangsu University, Zhenjiang, China
• ² University of Lakki Marwat, Lakki Marwat, Khyber Pakhtunkhwa, Pakistan
• ³ United Arab Emirates University, Al-Ain, Abu Dhabi, United Arab Emirates
• ⁴ King Saud University, Riyadh, Riyadh, Saudi Arabia
• ⁵ Ain Shams University, Cairo, Cairo, Egypt

This work aims to analyze the impacts of the magnetic field, activation of energy, thermal radiation, thermophoresis, and Brownian effects on the hybrid nanofluid (Ag+TiO$_2$+Silicon oil) flow past a porous spinning disk. The pressure loss due to porosity is constituted by the Darcy-Forchheimer relation. The modified Buongiorno model is considered for simulating the flow field into a mathematical form.} The modeled problem is further simplified with the new group of dimensionless variables and further transformed into \hl{a first-order} system of equations. The reduced system is further analyzed with \hl{the} Levenberg-Marquardt algorithm by using \textcolor{red}{a trained artificial neural network (ANN) with a tolerance $e^{-6}$, step size $0.001$ and $1000$ epochs.} The state variables under the impacts of the pertinent parameters are assessed with graphs and tables. It has been observed that when the magnetic parameter \textcolor{red}{increases}, the velocity gradient of mono and hybrid nanofluids decreases. As the input of the Darcy-Forchheimer parameter increases, the velocity profiles decrease. The result shows that as the thermophoresis parameter increases, temperature and concentration rise as well. When the activation energy parameter rises, the concentration profile becomes higher. For a deep insight \hl{into} the analysis of the problem, a statistical approach for the data fitting in the form of regression \hl{lines} and error \hl{histograms} for nanofluid (NF) and hybrid nanofluid (HNF) are presented. The regression lines show that $100\%$ of the data is utilized in the curve fitting, while the error histograms \hl{depict} the minimal zero error $-7.1e{-6}$ for the increasing values of $Nt$. Furthermore, the mean square error and performance validation for each varying parameter \hl{are} presented. For validation, the present results are compared with the available literature in the form of a table\textcolor{red}{, where the current results show great agreement with the existing one.