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This study introduces a new physics-informed neural networks (PINN)-based prediction method to determine the temperature pattern of fluid and fins when flow passes over plate-circular/ plate-square pin fin heat sinks (PCPFHS / PSPFHS). The proposed method is based on calculating the velocity pattern on the fins' surface. For this target, a training algorithm based on the feed-forward neural network (FNN) (110 layers of learnable weights and 16 neurons in each layer), a nonlinear activation function (rectified linear unit, "ReLU") and the Adam method for optimization is used. The training algorithm is fed by transient large eddy simulation (LES) results at every 0.01 s time step for the total physical time of 100 s. According to the input parameter type, the training: validation ratio is varied between 70:30 and 90:10 in order to keep the coefficient of determination (R2) at its maximum. The automatic differentiation employed the forward accumulation approach to reduce calculation costs, while the transient training matrix fed the neural network. The adaptive gradient (AdaGrad) method is also to improve convergence process and its speed up. Based on the developed calculation tools, the temperature pattern for the flow and over the fins are calculated according to the energy balance on the fin surface and the transient pattern of velocity predicted by PINN. After careful validation with experimental data and sensitivity analysis on the number of neurons and layers, the thermal behavior of PCPFHS and PSPFHS are determined using the conduction heat transfer equation inside the fins via the finite element method and by assuming a heat balance between the fins' surface and airflow. As a result of the proposed method, it is possible to reduce the number of equations in the calculation process of these parameters. According to the results, it is found that PSPFHS has an average Nusselt number which is 9.63% greater than the one in PCPFHS. However, compared to PCPFHS, PSPFHS shows a -17.78% reduced vorticity ratio at Re = 4,865. The results indicated that, for long calculation times (for instance, at 2,000 s physical time), the PINN method reduces calculation costs up to 35% compared to the technique that directly solves the energy conservation in the whole domain.