A closure for the master equation starting from the dynamic cavity method

. We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner, and which performs better on several important classes of problems.

[1]  A. Lage-Castellanos,et al.  Dynamics of epidemics from cavity master equations: Susceptible-infectious-susceptible models. , 2022, Physical review. E.

[2]  R. Mulet,et al.  From random point processes to hierarchical cavity master equations for stochastic dynamics of disordered systems in random graphs: Ising models and epidemics. , 2021, Physical review. E.

[3]  R. Mulet,et al.  The cavity master equation: average and fixed point of the ferromagnetic model in random graphs , 2020, Journal of Statistical Mechanics: Theory and Experiment.

[4]  Erik Aurell,et al.  Exploring the diluted ferromagnetic p-spin model with a cavity master equation. , 2018, Physical review. E.

[5]  S. Franz,et al.  Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics. , 2015, Physical review. E.

[6]  E. Aurell,et al.  Cavity master equation for the continuous time dynamics of discrete-spin models. , 2016, Physical review. E.

[7]  F. Ricci-Tersenghi,et al.  A simple analytical description of the non-stationary dynamics in Ising spin systems , 2016, 1607.05242.

[8]  Alessandro Ingrosso,et al.  The patient-zero problem with noisy observations , 2014, 1408.0907.

[9]  Lenka Zdeborová,et al.  Inferring the origin of an epidemy with dynamic message-passing algorithm , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  A. Pelizzola.  Variational approximations for stationary states of Ising-like models , 2013, 1307.6684.

[11]  Riccardo Zecchina,et al.  Optimizing spread dynamics on graphs by message passing , 2012, 1203.1426.

[12]  I. Neri,et al.  The cavity approach to parallel dynamics of Ising spins on a graph , 2009, 0905.3260.

[13]  Hong Qian,et al.  Chemical Biophysics: Quantitative Analysis of Cellular Systems , 2008 .

[14]  Akira Onuki,et al.  Phase Transition Dynamics , 2000 .

[15]  S. Kak.  Information, physics, and computation , 1996 .

[16]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[17]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[18]  鈴木 増雄.  Time-Dependent Statistics of the Ising Model , 1965 .