Coffee extraction is a complex process involving the flow of hot water through a porous coffee bed, where mass transfer, diffusion, and chemical reactions play a critical role. Traditional numerical methods for modeling this process can be computationally expensive and sensitive to mesh design, limiting their scalability and real-time applicability. Physics-Informed Neural Networks (PINNs) offer a promising alternative by embedding the governing advection-diffusion-reaction (ADR) equations directly into the learning process to predict the numerical solution. This approach allows for fast inference once the model is trained, reducing the need for dense, high-resolution data while maintaining physical consistency. However, PINNs can be challenging to train without additional information to anchor the solution space, potentially leading to poor convergence and inaccurate predictions. In this talk, we will explore the use of PINNs for coffee extraction modeling, highlighting their advantages for rapid simulation and the critical challenges associated with achieving accurate and stable convergence. This work can pave the way for extending the use of PINNs to even more complex differential systems, unlocking new possibilities in scientific modeling and industrial applications.