Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow
Xiaodong Feng, Li Zeng, Tao Zhou Tao Zhou
Abstract
In this work, we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck (TFP) equations. It is well known that solutions of such equations are probability density functions, and thus our approach relies on modelling the target solutions with the temporal normalizing flows. The temporal normalizing flow is then trained based on the TFP loss function, without requiring any labeled data. Being a machine learning scheme, the proposed approach is mesh-free and can be easily applied to high dimensional problems. We present a variety of test problems to show the effectiveness of the learning approach.
Topics & Concepts
Flow (mathematics)Fokker–Planck equationComputer scienceApplied mathematicsProbability density functionVariety (cybernetics)Statistical physicsFunction (biology)Mathematical optimizationMathematicsArtificial intelligencePhysicsMathematical analysisPartial differential equationStatisticsGeometryBiologyEvolutionary biologyModel Reduction and Neural NetworksGaussian Processes and Bayesian InferenceNeural Networks and Applications