Microalgal based processes are increasingly used to provide new compounds for the pharmaceutical, cosmetic, feed and food industries. Microalgae use light energy to fix carbon from CO2 to convert it into chemical energy. Then, to model the growth of microalgae inside a photobioreactor, light is a key factor. At the same time, it is a complex problem since the distribution of light intensity (the photons available for photosynthesis) is not uniform due to the self-shading of the cells and the turbidity of the medium. Also, the geometry of the photobioreactor and the mixing device must be considered to develop a physic-based model. To make the problem more complex, not only light intervenes in the growth of microalgae, but also other factors such as temperature, pH, etc. Physics-informed neural networks (PINNs) are a recent and powerful tool to solve problems involving differential equations. The fundamental idea is to leverage laws of physics written as differential equations in the training of neural networks. This hybrid approach overcome the limitations of pure machine learning models, which cannot capture physical principles that govern the phenomena. On the other side, physics-based modeling, are sensible to errors and uncertainly in measurement. Moreover, no model can exactly imitate a physical phenomenon due to some simplifications to reduce the model complexity. In biochemical systems, the limitations of physics-based models are more clear. We present a class of hybrid models that are suitable for the modeling of microalgae growth, combining first-principles physics-based models and artificial neural networks. Ordinary differential equations are used to model the physical phenomena that are solved numerically though a recurrent neural network capable to implement Runge-Kutta methods. The model is flexible enough to be implemented fully informed, i.e., no machine learning model is staged, which is equivalent to a physic-based model, or the dynamics can be fully estimated with a neural network. We focus in the hybrid scheme, where we chose Monod-like dynamics to model the growth rate that is corrected with a neural network. This approach is illustrated with artificial data from a detailed mechanistic model and from real data.