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

Finding accurate solutions to partial differential equations (PDEs) is acrucial task in all scientific and engineering disciplines. It has recentlybeen shown that machine learning methods can improve the solution accuracy bycorrecting for effects not captured by the discretized PDE. We target theproblem of reducing numerical errors of iterative PDE solvers and comparedifferent learning approaches for finding complex correction functions. We findthat previously used learning approaches are significantly outperformed bymethods that integrate the solver into the training loop and thereby allow themodel to interact with the PDE during training. This provides the model withrealistic input distributions that take previous corrections into account,yielding improvements in accuracy with stable rollouts of several hundredrecurrent evaluation steps and surpassing even tailored supervised variants. Wehighlight the performance of the differentiable physics networks for a widevariety of PDEs, from non-linear advection-diffusion systems tothree-dimensional Navier-Stokes flows.

Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers