Consistency and convergence of simulation schemes in information field dynamics

Martin Dupont and Torsten Enßlin
Phys. Rev. E 98, 043307 – Published 22 October 2018

Abstract

We explore a new simulation scheme for partial differential equations (PDE's) called information field dynamics (IFD). Information field dynamics is a probabilistic numerics method that seeks to preserve the maximum amount of information about the field being simulated. It rests on Bayesian field inference and therefore allows the incorporation of prior knowledge on the field. This makes IFD attractive to address the closure problem of simulations—how to incorporate knowledge about subgrid dynamics into a scheme on a grid with limited resolution. Here we analytically prove that a restricted subset of simulation schemes in IFD are consistent and thus deliver valid predictions in the limit of high resolutions. This has not previously been done for any IFD schemes. This restricted subset is roughly analogous to traditional fixed-grid numerical PDE solvers, given the additional restriction of translational symmetry. Furthermore, given an arbitrary IFD scheme modeling a PDE, it is a priori not obvious to what order the scheme is accurate in space and time. For this subset of models, we also derive an easy rule of thumb for determining the order of accuracy of the simulation. As with all analytic consistency analysis, an analysis for nontrivial systems is intractable; thus these results are intended as a general indicator of the validity of the approach, and it is hoped that the results will generalize.

  • Figure
  • Received 26 June 2018

DOI:https://doi.org/10.1103/PhysRevE.98.043307

©2018 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Martin Dupont and Torsten Enßlin

  • Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 98, Iss. 4 — October 2018

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×