Tensor network methods for solving the Vlasov equation

It has been proposed that tensor networks can be used to approximately solve partial differential equations with exponential speed-up, provided that the PDE is compressible and can be efficiently represented within the tensor network framework. Previously, we presented results on 2-D simulations of the Vlasov equation, which provides an ab-initio description of high-temperature plasmas. Here, we consider simulations in up to 6-D and analyze the performance of the tensor network methods in these higher dimensional calculations. For the test cases studied, we find that we are able to capture important features of the dynamics even with significant amounts of compression.