Multi-Agent Learning of Numerical Methods for Hyperbolic PDEs with Factored Dec-MDP
Abstract
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.
Keywords
Cite
@article{arxiv.2205.15716,
title = {Multi-Agent Learning of Numerical Methods for Hyperbolic PDEs with Factored Dec-MDP},
author = {Yiwei Fu and Dheeraj S. K. Kapilavai and Elliot Way},
journal= {arXiv preprint arXiv:2205.15716},
year = {2022}
}
Comments
Submitted to 20th International Conference on Practical Applications of Agents and Multi-Agent Systems (PAAMS 2022)