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

Numerical simulation is indispensable in industrial design processes. It canreplace expensive experiments and even reduce the need for prototypes. Whileproducts designed with the aid of numerical simulation undergo continuousimprovement, this must also be true for numerical simulation itself. Up todate, no general purpose numerical method is available which can accuratelyresolve a variety of physics ranging from fluid to solid mechanics includinglarge deformations and free surface flow phenomena. These complex multi-physicsproblems occur for example in Additive Manufacturing processes. In this sense,the recent developments in Machine Learning display promise for numericalsimulation. It has recently been shown that instead of solving a system ofequations as in standard numerical methods, a neural network can be trainedsolely based on initial and boundary conditions. Neural networks are smooth,differentiable functions that can be used as a global ansatz for PartialDifferential Equations (PDEs). While this idea dates back to more than 20 yearsago [Lagaris et al., 1998], it is only recently that an approach for thesolution of time dependent problems has been developed [Raissi et al., 2019].With the latter, implicit Runge Kutta schemes with unprecedented high orderhave been constructed to solve scalar-valued PDEs. We build on theaforementioned work in order to develop an Updated Lagrangian method for thesolution of incompressible free surface flow subject to the inviscid Eulerequations. The method is easy to implement and does not require any specificalgorithmic treatment which is usually necessary to accurately resolve theincompressibility constraint. Due to its meshfree character, we will name itthe Neural Particle Method (NPM). It will be demonstrated that the NPM remainsstable and accurate even if the location of discretization points is highlyirregular.

The Neural Particle Method -- An Updated Lagrangian Physics Informed Neural Network for Computational Fluid Dynamics