Model pathway diagrams for the representation of mathematical models

  • Thomas Koprucki
  • Michael Kohlhase
  • Karsten Tabelow
  • Dennis Müller
  • Florian Rabe
Part of the following topical collections:
  1. 2017 Numerical Simulation of Optoelectronic Devices


Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machine-actionable as well as human-understandable representation of the mathematical knowledge they contain and the domain-specific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the van Roosbroeck system describing the carrier transport in semiconductors by drift and diffusion. We introduce an approach for the block-based composition of models from simpler components.


Mathematical models Research data Model pathway diagrams Drift–diffusion equations 



We gratefully acknowledge EU funding for the OpenDreamKit project in the Horizon 2020 framework under Grant 676541 as well as DFG funding under Grant RA-18723-1 OAF. Our discussions have particularly profited from contributions by Wolfram Sperber (general math background).


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Authors and Affiliations

  1. 1.Weierstrass Institute (WIAS)BerlinGermany
  2. 2.InformatikFAU Erlangen-NürnbergErlangenGermany
  3. 3.Jacobs University BremenBremenGermany

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