  We explore a new simulation scheme for partial differential equations (PDE's)
called Information Field Dynamics (IFD). Information field dynamics attempts to
improve on existing simulation schemes by incorporating Bayesian field
inference, which seeks to preserve the maximum amount of information about the
field being simulated. The field inference is truly Bayesian and thus depends
on a notion of prior belief. 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 modelling 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.
