A Tensor Decomposition Method for High Dimensional Fokker-Planck Equation Modeling Polymeric Liquids

The multi-bead-spring (MBS) model for polymeric liquids is commonly employed to represent the coarse-grained molecular configuration characterized by the Fokker-Planck Equation (FPE). For chain consisting of several beads, the state space involved in the resulting transient FPE would become rather high dimensional. And solving this high dimensional FPE is a challenging task even on supercomputers due to curse of dimensionality. In this paper, a tensor decomposition approach combined with Chebyshev spectral differentiation is used to tackle this problem, where the transient solution is sought in the CANDECOMP/PARAFAC decomposition form by the alternating least squares algorithm, and the temporal dimension is treated (and hence decoupled) in the same manner as all other spatial dimensions. This tensor method drastically reduces the degrees of freedom required in the solution process. Numerical results for MBS models with 3D and 9D sate spaces are provided by implementing this tensor method on a regular PC.

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