Abstract: We have developed a physics informed neural network to handle inverse optimal control problems in differential games with Nash equilibrium, called Nash Neural Networks (N3) [1]. Following recent work on Hamiltonian and Lagrangian Neural Networks, we build the game dynamics into the structure of the network, which allows us to automatically derive the governing equations from black-box utility functions. This N3 framework can then be used to infer utilities from optimal behavior, without having to specify the functional form of the (unknown) utility. We have used the N3 to analyze the optimal social-distancing behaviour of individuals in a pandemic, by training against synthetic data generated from a known model [2]. We were able to accurately infer the individual payoff function, which contained a social distancing cost and an infection cost, as well as its functional dependence on the population/individual state parameters.
[1] Nash Neural Networks: Inferring utilities from optimal behavior 2022, J. J. Molina et al., preprint [https://arxiv.org/abs/2203.13432]
[2] Rational social distancing policy during epidemics with limited healthcare capacity
2022, S. K. Schnyder et al., under review