  Factored decentralized Markov decision process (Dec-MDP) is a framework for
modeling sequential decision making problems in multi-agent systems. In this
paper, we formalize the learning of numerical methods for hyperbolic partial
differential equations (PDEs), specifically the Weighted Essentially
Non-Oscillatory (WENO) scheme, as a factored Dec-MDP problem. We show that
different reward formulations lead to either reinforcement learning (RL) or
behavior cloning, and a homogeneous policy could be learned for all agents
under the RL formulation with a policy gradient algorithm. Because the trained
agents only act on their local observations, the multi-agent system can be used
as a general numerical method for hyperbolic PDEs and generalize to different
spatial discretizations, episode lengths, dimensions, and even equation types.
