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Autoencoder-assisted study of directed percolation with spatial long-range interactions

by Yanyang Wang, Yuxiang Yang, Wei Li

Submission summary

Authors (as registered SciPost users):

Yanyang Wang

Abstract

In the field of non-equilibrium phase transitions, the classification problem of reaction-diffusion processes with long-range interactions is both challenging and intriguing. Determining critical points serves as the foundation for studying the phase transition characteristics of these universality classes. In contrast to Monte Carlo simulations of statistical system observables, machine learning methods can extract evolutionary information from clusters of such systems, thereby rapidly identifying phase transition regions. We have developed a new method that uses one-dimensional encoded results of the stacked autoencoder to determine critical points, and it has a high level of reliability. Subsequently, the critical exponent $\delta$ of particle survival probability and the characteristic time $t_f$ of finite-scale systems can be measured. Utilizing the scaling relation $t_f{\sim}L^{z}$ yields the dynamic exponent $z$. Finally, we discuss an alternative method adopting L{\'{e}}vy distribution to generate random walk steps, inserting another global expansion mechanism. The critical points obtained through it are very close to the predictions of field theory. This study suggests promising applications of autoencoder methods in processes involving such long-range interactions.

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• Provide a novel and synergetic link between different research areas.
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• Detail a groundbreaking theoretical/experimental/computational discovery
• Present a breakthrough on a previously-identified and long-standing research stumbling block