Large-scale neural solvers for partial differential equations

Publikation: Beitrag in Buch/Konferenzbericht/Sammelband/GutachtenBeitrag in KonferenzbandBeigetragenBegutachtung


  • Patrick Stiller - , Helmholtz-Zentrum Dresden-Rossendorf, Technische Universität Dresden (Autor:in)
  • Friedrich Bethke - , Helmholtz-Zentrum Dresden-Rossendorf, Technische Universität Dresden (Autor:in)
  • Maximilian Böhme - , Center for Advanced Systems Understanding (CASUS) (Autor:in)
  • Richard Pausch - , Helmholtz-Zentrum Dresden-Rossendorf (Autor:in)
  • Sunna Torge - , Zentrum für Informationsdienste und Hochleistungsrechnen (ZIH), Technische Universität Dresden (Autor:in)
  • Alexander Debus - , Helmholtz-Zentrum Dresden-Rossendorf (Autor:in)
  • Jan Vorberger - , Helmholtz-Zentrum Dresden-Rossendorf (Autor:in)
  • Michael Bussmann - , Helmholtz-Zentrum Dresden-Rossendorf, Center for Advanced Systems Understanding (CASUS) (Autor:in)
  • Nico Hoffmann - , Helmholtz-Zentrum Dresden-Rossendorf (Autor:in)


Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modeled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation as well as sophisticated, tailored code for distributed computing. Scanning the parameters of the underlying model significantly increases the runtime as the simulations have to be cold-started for each parameter configuration. Machine Learning based surrogate models denote promising ways for learning complex relationship among input, parameter and solution. However, recent generative neural networks require lots of training data, i.e. full simulation runs making them costly. In contrast, we examine the applicability of continuous, mesh-free neural solvers for partial differential equations, physics-informed neural networks (PINNs) solely requiring initial/boundary values and validation points for training but no simulation data. The induced curse of dimensionality is approached by learning a domain decomposition that steers the number of neurons per unit volume and significantly improves runtime. Distributed training on largescale cluster systems also promises great utilization of large quantities of GPUs which we assess by a comprehensive evaluation study. Finally, we discuss the accuracy of GatedPINN with respect to analytical solutionsas well as state-of-the-art numerical solvers, such as spectral solvers.


TitelDriving Scientific and Engineering Discoveries Through the Convergence of HPC, Big Data and AI - 17th Smoky Mountains Computational Sciences and Engineering Conference, SMC 2020, Revised Selected Papers
Redakteure/-innenJeffrey Nichols, Arthur ‘Barney’ Maccabe, Suzanne Parete-Koon, Becky Verastegui, Oscar Hernandez, Theresa Ahearn
Herausgeber (Verlag)Springer Science and Business Media B.V.
ISBN (Print)9783030633929
PublikationsstatusVeröffentlicht - 2021


ReiheCommunications in Computer and Information Science
Band1315 CCIS


Titel17th Smoky Mountains Computational Sciences and Engineering Conference, SMC 2020
Dauer26 - 28 August 2020
StadtVirtual, Online

Externe IDs

ORCID /0000-0001-9756-6390/work/142250111