Abstract: Control problems for ordinary differential equations describe epidemic, social and other physics processes. After study of identifiability and sensitivity of SIR models, well-posedness in proximity of exact solution and convergence of classical numerical schemes we propose several scenarios of possible epidemic outcome and formulate of the optimal control problem. The usage of physically informed neural nets substantially decreases necessary man-hours to present characteristics of a differential equation, and total computational time, if according to hardware (GPUs) is available. The proposed deep learning algorithm is compared to classical collocation approach. It is used in the most numerically challenging part of the problem, the nonlinear HJB partial differential equation, while classical methods are applied to main ODE part of SIR-based model. Numerical results show substantial effect of induced control in decrease of total number of infected and time of active spread of epidemic.

Cite: Neverov A.V. , Krivorotko O.I. , Кабанихин С.И.
Neural nets for forecasting of scenarios and control of epidemics
Математика искусственного интеллекта 24-28 Mar 2025