English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we propose a deep learning-based method, deep Euler method(DEM) to solve ordinary differential equations. DEM significantly improves theaccuracy of the Euler method by approximating the local truncation error withdeep neural networks which could obtain a high precision solution with a largestep size. The deep neural network in DEM is mesh-free during training andshows good generalization in unmeasured regions. DEM could be easily combinedwith other schemes of numerical methods, such as Runge-Kutta method to obtainbetter solutions. Furthermore, the error bound and stability of DEM isdiscussed.

Deep Euler method: solving ODEs by approximating the local truncation error of the Euler method