1206.4229 (Torsten A. Enßlin)
Torsten A. Enßlin
Information field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields. Any simulation scheme updates a discretized field representation, the data in a computer's memory, for the next time step according to a discretized, approximate representation of the underlying field dynamics. Assumptions about the continuum field behavior on sub-grid scales are reflected in these rules, e.g. the field might be assumed to be constant within a grid cell, or to be some weighted average of neighboring data points, and the like. In contrast to such parametrized sub-grid field structures, IFD constructs non-parametric sub-grid field configurations from the combination of the data, representing constraints on possible field configurations, and prior assumptions on the sub-grid field statistics. Each of these field configurations can formally be evolved to a later moment since any differential operator of the dynamics can act on fields living in continuous space. However, these virtually evolved fields need again a representation by data in computer memory. The maximum entropy principle guides the construction of updated datasets via entropic matching, optimally representing these field configurations at the later time. The field dynamics thereby become represented by a finite set of evolution equations for the data that can be solved numerically. These should provide a more accurate description of the physical field dynamics, due to the more rigorous accounting of sub-grid physics and the space discretization process. The IFD approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical Klein-Gordon field. The next steps towards the construction of IFD simulation schemes for more complex systems, e.g. for turbulent hydrodynamics, are also briefly discussed here.
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http://arxiv.org/abs/1206.4229
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