Efficient and Scalable Prediction of Stochastic Reaction–diffusion Processes Using Graph Neural Networks
Mathematical Biosciences(2024)
摘要
The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction–diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction–diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction–diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading.
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关键词
Reaction–diffusion,Master equation,Neural networks
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