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arXiv · 2205.15716

Multi-Agent Learning of Numerical Methods for Hyperbolic PDEs with Factored Dec-MDP

Yiwei Fu·Dheeraj S. K. Kapilavai·Elliot Way
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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.

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Yiwei Fu, Dheeraj S. K. Kapilavai, Elliot Way. 2022-05-31. Multi-Agent Learning of Numerical Methods for Hyperbolic PDEs with Factored Dec-MDP. https://doi.org/10.1007/978-3-031-18192-4_15

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