Non-Parametric Belief Propagation Solver for Stochastic Systems of Linear Equations

The striking growth of powerful computing resources allows time-efficient solution of computationally demanding problems. In particular, advances in high-performance computing have made stochastic approaches to real-world applications more practical. The belief propagation (BP) algorithm is a probabilistic method typically used in information theory and artificial intelligence. This article exploits the probabilistic message passing attribute of BP for solving stochastic linear systems that naturally arise from finite element formulation of stochastic partial differential equations (PDEs), establishing an explicit connection between the two fields for the first time. The accuracy of the algorithm is validated by comparison to the well-known Monte Carlo method.