Learning to differentiate
| Autor: | Gianluca Iaccarino, Jan Nordström, Oskar Ålund |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Theoretical computer science Physics and Astronomy (miscellaneous) Artificial neural network Summation by parts Computer science Applied Mathematics Stability (learning theory) 010103 numerical & computational mathematics Construct (python library) Differential operator 01 natural sciences Computer Science Applications 010101 applied mathematics Computational Mathematics Modeling and Simulation Linear algebra Polygon mesh 0101 mathematics Regression algorithm |
| Zdroj: | Journal of Computational Physics. 424:109873 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2020.109873 |
| Popis: | Artificial neural networks together with associated computational libraries provide a powerful framework for constructing both classification and regression algorithms. In this paper we use neural networks to design linear and non-linear discrete differential operators. We show that neural network based operators can be used to construct stable discretizations of initial boundary-value problems by ensuring that the operators satisfy a discrete analogue of integration-by-parts known as summation-by-parts. Our neural network approach with linear activation functions is compared and contrasted with a more traditional linear algebra approach. An application to overlapping grids is explored. The strategy developed in this work opens the door for constructing stable differential operators on general meshes. |
| Databáze: | OpenAIRE |
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