This article investigates solar energy storage due to the Jeffrey hybrid nanofluid flow containing gyrotactic microorganisms through a porous medium for parabolic trough solar collectors. The mechanism of thermophoresis and Brownian motion for the graphene and silver nanoparticles are also encountered in the suspension of water-based heat transfer fluid. The gyrotactic microorganisms have the ability to move in an upward direction in the nanofluid mixture, which enhances the nanoparticle stability and fluid mixing in the suspension. Mathematical modeling of the governing equations uses the conservation principles of mass, momentum, energy, concentration, and microorganism concentration. The non-similar variables are introduced to the dimensional governing equations to get the non-dimensional ordinary differential equations. The Cash and Carp method is implemented to solve the non-dimensional equations. The artificial neural network is also developed for the non-dimensional governing equations using the Levenberg Marquardt algorithm. Numerical findings corresponding to the diverse parameters influencing the nanofluid flow and heat transfer are presented in the graphs. The thermal profiles are observed to be enhanced with the escalation in the Darcy and Forchheimer parameters. And the Nusselt number enhances with the escalation in the Deborah number and retardation time parameter. Entropy generation reduces with an enhancement in Deborah number and retardation time parameter. Solar energy is the best renewable energy source. It can fulfill the energy requirements for the growth of industries and engineering applications.