Nonlinear Fokker-Planck Equations: Fundamentals and Applications

By T. Frank. 2004

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A Free Energy Principle for Biological Systems (2012, background): “In synergetics and the study of self-organizing systems [46,47], one could associate the external states with microscopic system variables (stable modes) that show fast fluctuations, while the internal states might correspond to the macroscopic order parameters (unstable modes) that enslave them.”
Stochastic Gradient Descent Performs Variational Inference, Converges to Limit Cycles for Deep Networks (2017, background): “It can be shown (Frank, 2005, Sec.”
A free energy principle for a particular physics (2019, methodology): “The associated NESS density ( )p x is the solution to the Fokker-Planck equation (Frank, 2004).”
Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations (2007, unknown): “In order to make the connection between the second order variations (182) and (193), the idea is to project the perturbation δf on a suitable space and write δf = δfk + δf⊥ where δf⊥ is the orthogonal perturbation (this is a relatively general method that has been applied in different contexts; see ”