Solving for high dimensional committor functions using artificial neural networks
arXiv:1802.10275
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.
arXiv comment12 pages, 6 figures
References in corpus (6)
- Adam: A Method for Stochastic Optimization
- Deep Learning in Neural Networks: An Overview
- TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems
- DGM: A deep learning algorithm for solving partial differential equations
- A unified deep artificial neural network approach to partial differential equations in complex geometries
- Point cloud discretization of Fokker-Planck operators for committor functions