A state-space approach to analyze structural uncertainty in physical models

Physics-based computer models, such as fluid flow simulations, seek to approximate the behavior of a real system based on the physical equations that govern the evolution of that system. The model approximation of reality, however, is imperfect because it is subject to uncertainties coming from different sources: finite model resolution, uncertainty in model parameter values, uncertainty in input data such as external forgings, and uncertainty in the structure of the model itself. Many studies to date have considered the effects of parameter and data uncertainty on model outputs, and have offered solutions to obtain the best fitted parameter values for a model. However, much less effort has been devoted to the study of structural uncertainty, which is caused by our incomplete knowledge about the true physical processes, and manifests itself as missing dynamics in the model. This paper seeks to understand structural uncertainty by studying the observable errors, i.e. the discrepancies between the model solutions and measurements of the physical system. The dynamics of these errors is modeled using a state-space approach, which enables one to identify the source of uncertainty and to recognize the missing dynamics inside model. Furthermore, the model solution can be improved by correcting it with the error predicted by the state-space approach. The proposed methodology is applied to two test problems, Lorenz-96 and a stratospheric chemistry model.