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/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

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

Zendy Tools

Zendy Open

With the remarkable empirical success of neural networks across diversescientific disciplines, rigorous error and convergence analysis are also beingdeveloped and enriched. However, there has been little theoretical workfocusing on neural networks in solving interface problems. In this paper, weperform a convergence analysis of physics-informed neural networks (PINNs) forsolving second-order elliptic interface problems. Specifically, we considerPINNs with domain decomposition technologies and introduce gradient-enhancedstrategies on the interfaces to deal with boundary and interface jumpconditions. It is shown that the neural network sequence obtained by minimizinga Lipschitz regularized loss function converges to the unique solution to theinterface problem in $H^2$ as the number of samples increases. Numericalexperiments are provided to demonstrate our theoretical analysis.

Convergence of physics-informed neural networks applied to linear second-order elliptic interface problems