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A common goal in the study of high dimensional and complex system is to modelthe system by a low order representation. In this letter we propose a generalapproach for assessing the quality of a reduced order model for highdimensional chaotic systems. The key of this approach is the use of optimalshadowing, combined with dimensionality reduction techniques. Rather thanquantify the quality of a model based on the quality of predictions, which canbe irrelevant for chaotic systems since even excellent models can do poorly, wesuggest that a good model should allow shadowing by modeled data for longtimes; this principle leads directly to an optimal shadowing criterion of modelreduction. This approach overcomes the usual difficulties encountered bytraditional methods which either compare systems of the same size bynormed-distance in the functional space, or measure how close an orbitgenerated by a model is to the observed data. Examples include intervalarithmetic computations to validate the optimal shadowing.

Judging Model Reduction of Chaotic Systems via Optimal Shadowing Criteria