Active Learning Based Sampling for High-Dimensional Nonlinear Partial Differential Equations

Understand

The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs).

• However, this method usually converges slowly.
• To speed up the convergence of this approach, an active-learning-based sampling algorithm is proposed in this paper.
• This algorithm actively chooses the most informative training samples from a probability density function based on residual errors to facilitate error reduction.