Matrix Product State Simulation of Reactive Flows

The matrix product state (MPS) representation, developed for approximating quantum many-body systems, exploits their correlation structure to accurately capture the underlying physics in a low-rank form (i.e., in a massively reduced state space). Here, the methodology is invoked to simulate several reactive flow systems. The flow fields and governing differential operators are recast in the context of MPS, and their dynamics is simulated for various degrees of truncation. The generated MPS-reduced order solutions are appraised against the results obtained via direct numerical simulation of the original equations. The computational complexity of MPS is assessed to determine its potential for calculating complex multi-scale turbulent reacting flows.