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Abstract:
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This talk investigates model building in dynamical systems. In many contexts, systems of nonlinear differential equations have been proposed to model complex behavior. These equations have had remarkable success at mimicking the qualitative features of observed systems. However, they frequently exhibit poor quantitative performance. I investigate diagnostics for nonlinear differential equations. In particular, I show that the estimation of lack of fit can be appropriately measured in terms of latent inputs into the dynamical system. In this talk, I discuss the analysis of such inputs for the discovery of missing dynamical variables. The machinery of Chaotic Data Analysis may be employed here to derive a diagnostic for missing components. However, results from dynamical systems theory also suggest that care should be taken when modifying systems to account for such discoveries.
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