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

Developing fast surrogates for Partial Differential Equations (PDEs) willaccelerate design and optimization in almost all scientific and engineeringapplications. Neural networks have been receiving ever-increasing attention anddemonstrated remarkable success in computational modeling of PDEs, however;their prediction accuracy is not at the level of full deployment. In this work,we utilize the transformer architecture, the backbone of numerousstate-of-the-art AI models, to learn the dynamics of physical systems as themixing of spatial patterns learned by a convolutional autoencoder. Moreover, weincorporate the idea of multi-scale hierarchical time-stepping to increase theprediction speed and decrease accumulated error over time. Our model achievessimilar or better results in predicting the time-evolution of Navier-Stokesequations compared to the powerful Fourier Neural Operator (FNO) and twotransformer-based neural operators OFormer and Galerkin Transformer.

Multi-scale Time-stepping of Partial Differential Equations with Transformers