<p>This article proposes a methodology for developing an artificial intelligence system for modeling protein interactions in biological systems based on reaction-diffusion equations with multivalued interaction functions. The primary goal of the research is to approximate the solutions to these equations using highly efficient computational methods, specifically, physics-informed neural networks (PINN) and the deep learning Galerkin method (DLGM). The proposed system utilizes machine learning to model complex biological processes while accounting for real cellular conditions. The authors have developed and rigorously justified a computational algorithm that, on the current level of mathematical rigor, ensures the approximation of solutions to infinite-dimensional stochastic optimization problems and demonstrates superior efficiency compared to traditional methods. The high accuracy and speed of the obtained results enable extending this methodology to other types of partial differential equations, particularly, for biological and medical applications.</p>