Semantic Scholar Open Access 2017 1742 sitasi

The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems

E. Weinan Ting Yu

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Abstrak

We propose a deep learning-based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz Method is naturally nonlinear, naturally adaptive and has the potential to work in rather high dimensions. The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning. We illustrate the method on several problems including some eigenvalue problems.

Topik & Kata Kunci

Computer Science Mathematics

Penulis (2)

E. Weinan

Ting Yu

Format Sitasi

APA MLA BibTeX

Weinan, E., Yu, T. (2017). The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems. https://doi.org/10.1007/s40304-018-0127-z

Akses Cepat

Lihat di Sumber doi.org/10.1007/s40304-018-0127-z

Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Total Sitasi: 1742×
Sumber Database: Semantic Scholar
DOI: 10.1007/s40304-018-0127-z
Akses: Open Access ✓