ArticleEntropy (Basel, Switzerland)2022
Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry.
Article in Entropy (Basel, Switzerland), 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Information Geometry Theoretic Measures for Characterizing Neural Information Processing from Simulated EEG Signals.Entropy (Basel, Switzerland) · 2024Article
- Stochastic Dynamics of Fusion Low-to-High Confinement Mode (L-H) Transition: Correlation and Causal Analyses Using Information Geometry.Entropy (Basel, Switzerland) · 2023Article
- Effects of Stochastic Noises on Limit-Cycle Oscillations and Power Losses in Fusion Plasmas and Information Geometry.Entropy (Basel, Switzerland) · 2023Article
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2 authors.
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Abstract
Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker-Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker-Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated.
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