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A numerical procedure for model reduction using the generalized Langevin equation formalism
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The Zwanzig-Mori pro jection formalism is widely used in studying systems with many degrees of freedom. Recently Xing and Kim used the pro jection formalism and derived the generalized Langevin equations (GLEs) for a general stochastic system not necessarily obeying detailed balance. In this study we develop a numerical procedure to reconstruct the GLEs from data. Numerical tests on two biological networks show remarkable agreement between the results calculated from the reconstructed GLEs and those of full model simulations. We suggest that the procedure can be applied in model reduction and a novel way of nonlinear time series analysis.
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Comparison of different exact generalized Langevin equations with a non-linear potential of mean force and an observable-dependent mass and friction
Four exact GLEs are compared that differ in whether the memory friction kernel depends on the observable and whether the potential includes the observable's effective kinetic energy, with the latter form preferred whe...
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