# Parametric Fokker-Planck equation

## TL;DR

This paper derives a parametric version of the Fokker-Planck equation as a Wasserstein gradient flow on the statistical manifold, simplifying it to a finite-dimensional ODE with analytical and numerical examples.

## Contribution

It introduces a novel derivation of the Fokker-Planck equation on parametric spaces, connecting PDEs with finite-dimensional ODEs on parameter manifolds.

## Key findings

- Derived the parametric Fokker-Planck equation as a Wasserstein gradient flow.
- Reduced the PDE to a finite-dimensional ODE on parameter space.
- Provided analytical and numerical examples demonstrating the approach.

## Abstract

We derive the Fokker-Planck equation on the parametric space. It is the Wasserstein gradient flow of relative entropy on the statistical manifold. We pull back the PDE to a finite dimensional ODE on parameter space. Some analytical example and numerical examples are presented.