Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract  present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations,  parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables.  show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory.  demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.
['Huan Lei', 'Nathan A. Baker', 'Xiantao Li']
I am writing a research paper on a idea Data-driven parameterization of the generalized Langevin equation
[{"from": "human", "value": "I am writing a research paper on a idea Data-driven parameterization of the generalized Langevin equation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract  present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations,  parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables.  show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory.  demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method."}]