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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 2: Focus Session: Machine Learning for Complex Socio-economic Systems

SOE 2.3: Vortrag

Montag, 18. März 2024, 10:15–10:30, MA 001

Inferring the Utility from Optimal Behaviour in an Epidemic using Neural Networks — •Mark Lynch¹, Matthew Turner², John Molina³, Simon Schnyder⁴, and Ryoichi Yamamoto³ — ¹Mathematics of Systems CDT, University of Warwick, Coventry, CV4 7AL, UK — ²Department of Physics, University of Warwick, Coventry, CV4 7AL, UK — ³Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan — ⁴Institute of Industrial Science, The University of Tokyo, Tokyo 153-8455, Japan

Many dynamical systems can be represented as differential games, where different interacting individuals are each seeking to simultaneously maximise their own utility function by modifying their behaviour. Here we consider rational individuals socially distancing in an epidemic. Given a specified form of utility, one can solve the related constrained optimal control problem to derive optimal system dynamics that result in the maximal utilities for each individual.

We seek to use Machine Learning techniques to solve the inverse problem, that of inferring some unknown utility function that is being optimised by given system dynamics. Usually this has been solved by assuming some fixed form of the utility. We propose a more ambitious machine learning framework that is able to infer this hidden utility assuming no knowledge of the form of this function. The main issue to address is how to perform the learning of such a function without knowledge of the hidden variables required to define the underlying constrained optimization problem (i.e., the Lagrange multipliers).

Keywords: Physics Informed Neural Networks; Epidemiology; Optimal Control Theory; Machine Learning