# Solving for high dimensional committor functions using artificial neural networks

## TL;DR

This paper introduces a neural network-based method to approximate high-dimensional committor functions, central to transition path theory, by solving associated Fokker-Planck equations through variational formulations and stochastic optimization.

## Contribution

It presents a novel neural network approach for high-dimensional committor functions, enabling feasible numerical solutions where traditional methods struggle.

## Key findings

- Moderate accuracy achieved for high-dimensional problems.
- Neural network approach effectively approximates solutions to complex PDEs.
- Method leverages variational formulation and stochastic optimization.

## Abstract

In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical schemes for the committor function, the central object of transition path theory, which satisfies a high-dimensional Fokker-Planck equation. By working with the variational formulation of such partial differential equation and parameterizing the committor function in terms of a neural network, approximations can be obtained via optimizing the neural network weights using stochastic algorithms. The numerical examples show that moderate accuracy can be achieved for high-dimensional problems.