Application of Physics-Informed Neural Networks in Optimal Control Problems of Biological Models

When solving the optimal control problem of biological models, the Pontryagin's Minimum Principle is an effective solution method. When this method is applied to solve the optimal control, a type of two-point boundary value ordinary differential equations (ODEs) involving control variables. One part of the equations gives the initial conditions at the beginning of the time interval, and the other part of the equations gives the final value conditions at the end of the time interval. This paper uses Physics-Informed Neural Networks (PINNs) to solve this type of special differential equations. By solving several exemplary classical control problems in biological models and comparing with the traditional Forward-Backward Sweep Method (FBSM), the effectiveness of PINNs in solving such differential equations is verified. This paper expands the application scenarios of PINNs and provides a new idea for solving optimal control problems.