Deep Learning for High-Dimensional Systems Governing Anomalous Diffusion

Source abstract

Anomalous diffusion in complex systems, such as intracellular transport and soft glassy materials, often emerges from coupled dynamics between a tracer particle and multiple internal states of its heterogeneous environment. We develop a deep learning framework based on backward stochastic differential equations to solve high-dimensional anomalous Fokker-Planck equations with numerous internal states in an unbounded domain. The transition matrices of internal states can be singular or non-singular; tailored algorithmic strategies are proposed for each case. The resulting scalable algorithms provide a way to probe the microscopic origins of anomalous diffusion in high-dimensional heterogeneous systems. Their effectiveness and accuracy are validated in several ways, depending on the number and dimension of the equations to be solved.