The alteration of the climate in various areas of the world is of increasing concern since climate stability is a necessary condition for human survival as well as every living organism. The main reason of climate change is the greenhouse effect caused by the accumulation of carbon dioxide in the atmosphere. In this paper, we design a networked system underpinned by compartmental dynamical thermodynamics to circulate the atmospheric carbon dioxide. Specifically, in the carbon dioxide emitter compartment, we develop an initial-condition-dependent finite-time stabilizing controller that guarantees stability within a desired time leveraging the system property of affinity in the control. Then, to compensate for carbon emissions we show that a cultivation of microalgae with a volume 625 times bigger than the one of the carbon emitter is required. To increase the carbon uptake of the microalgae, we implement the nonaffine-in-the-control microalgae dynamical equations as an environment of a state-of-the-art library for reinforcement learning (RL), namely, Stable-Baselines3, and then, through the library, we test the performance of eight RL algorithms for training a controller that maximizes the microalgae absorption of carbon through the light intensity. All the eight controllers increased the carbon absorption of the cultivation during a training of 200,000 time steps with a maximum episode length of 200 time steps and with no termination conditions. This work is a first step towards approaching net zero as a classical and learning-based network control problem. The source code is publicly available.