Advanced neural network modeling with Levenberg–Marquardt algorithm for optimizing tri-hybrid nanofluid dynamics in solar HVAC systems

The performance of photovoltaic (PV)-based heating, ventilation, and air conditioning (HVAC) systems is highly sensitive to operating temperature. To address this, we propose a nanofluid-based thermal cooling model and develop an advanced computational solver using an Artificial Neural Network (ANN) trained with the Levenberg–Marquardt algorithm (LMA-TNN). This model analyzes the magnetohydrodynamic (MHD) radiative flow of a rotating Sutterby tri-hybrid nanofluid, incorporating critical factors such as linear thermal radiation, boundary slip, and activation energy. The nonlinear differential equations derived from the physical model are solved using the three-step Lobatto IIIa method, ensuring precision and reliability. Reference data for the LMA-TNN solver are generated for various HVAC scenarios, with a focus on key parameters including Reynolds and Deborah numbers, radiation, temperature slip, and activation energy. The LMA-TNN model is rigorously trained, validated, and tested, achieving high accuracy in predicting numerical solutions for diverse HVAC operating conditions. The model's performance is evaluated using state transition (ST) index, error histogram (EH), mean squared error, and regression (R) analysis, demonstrating excellent agreement between predicted and reference solutions. The results show an error range of 10⁻⁷ to 10⁻¹¹, confirming the model's reliability and potential for optimizing PV-based HVAC systems.