Optimal control of agent-based models via surrogate modeling.

This paper describes and validates an algorithm to solve optimal control problems for agent-based models (ABMs). For a given ABM and a given optimal control problem, the algorithm derives a surrogate model, typically lower-dimensional, in the form of a system of ordinary differential equations (ODEs), solves the control problem for the surrogate model, and then transfers it back to the original ABM. It applies to quite general ABMs and offers several options for the ODE structure, depending on what information about the ABM is to be used. There is a broad range of applications for such an algorithm, since ABMs are used widely in the life sciences, such as ecology, epidemiology, and biomedicine and healthcare, areas where optimal control is an important purpose for modeling, such as for medical digital twin technology. Author summary: The motivation for the work reported in this paper is the development of mathematical tools for medical digital twin development. Based on a computational model of some aspects of human biology, there is a two-way interaction between the physical twin (the patient) and the digital twin (the model). In one direction, the model is periodically calibrated with patient-derived data to evolve together with the patient, making the model into a digital twin, and in the other direction, optimal interventions derived from the digital twin are administered to the patient. In many cases, the underlying computational model does not readily provide optimal control methods to identify interventions. Model types such as agent-based models (ABMs) are often more suitable than models consisting of ordinary differential equations (ODEs). In this paper, we present an algorithm that takes as input a general ABM, together with an optimal control problem and provides as output a solution. This is accomplished by first constructing a surrogate ODE model, solving the optimal control problem, and then lifting it to the ABM. The algorithm provides for several different types of surrogate models, ranging from those that implement mechanistic features of the ABM to purely phenomenological models. The algorithm is validated by applying it to a predator-prey ABM and a metabolic network represented as an ABM. [ABSTRACT FROM AUTHOR]