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Active learning based sampling for high-dimensional nonlinear partial differential equations
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DOI：10.1016/j.jcp.2022.111848.png)
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Abstract
En 中文
The deep-learning-based least squares method has shown successful results in solving high-dimensional and 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. In particular, points with larger residual errors will have more chances of being selected for training. This algorithm imitates the human learning process: learners are likely to spend more time repeatedly studying mistakes than other tasks they have correctly finished. A series of numerical results are illustrated to demonstrate the effectiveness of our active-learning-based sampling in high dimensions to speed up the convergence of the deep-learning-based least squares method.(c) 2022 Elsevier Inc. All rights reserved.
Keywords:
Deep learning
Active learning
Adaptive sampling
Nonlinear PDEs
High-dimensional
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