Information field dynamics for simulation scheme construction

Abstract

Information field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields without assuming a particular sub-grid structure as many schemes do. IFD constructs an ensemble of non-parametric sub-grid field configurations from the combination of the data in computer memory, 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 of information theory 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. The sub-grid dynamics is treated within an auxiliary analytic consideration and the resulting scheme acts solely on the data space. It should provide a more accurate description of the physical field dynamics than simulation schemes constructed ad-hoc, due to the more rigorous accounting of sub-grid physics and the space discretization process. Assimilation of measurement data into an IFD simulation is conceptually straightforward since measurement and simulation data can just be merged. The IFD approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical Klein-Gordon field. This should pave the way towards the construction of schemes for more complex systems like turbulent hydrodynamics.