| Autor: |
Siddhartha Mishra |
| Jazyk: |
angličtina |
| Rok vydání: |
2018 |
| Předmět: |
|
| Zdroj: |
Mathematics in Engineering, Vol 1, Iss 1, Pp 118-146 (2018) |
| Druh dokumentu: |
article |
| ISSN: |
2640-3501 |
| DOI: |
10.3934/Mine.2018.1.118/fulltext.html |
| Popis: |
We propose a machine learning framework to accelerate numerical computations oftime-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existingnumerical methods as artificial neural networks, with a set of trainable parameters. These parametersare determined in an offline training process by (approximately) minimizing suitable (possibly non-convex)loss functions by (stochastic) gradient descent methods. The proposed algorithm is designed tobe always consistent with the underlying differential equation. Numerical experiments involving bothlinear and non-linear ODE and PDE model problems demonstrate a significant gain in computational efficiency over standard numerical methods. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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