Machine-Learning surrogates for information geometric analysis of multi-parameter models*

Information theoretic tools are emerging as an important class of model-analysis methods. These include tools such as the Fisher Information Matrix (FIM) and information geometric techniques for model selection and parameter identifiability analysis. Critical to these methods is the ability to evaluate derivatives of the model predictions with respect to model parameters. Finite difference methods are often not sufficiently accurate, and so modern automatic differentiation (AD) methods are an enabling technology for these information theoretic analyses. However, many models are available only as "legacy code" to which AD methods are difficult to apply. To utilize these AD methods, we propose a general method in which a machine learned model is used as a surrogate model for these legacy models. We demonstrate this method for a legacy model that calculates underwater acoustic transmission loss in an ocean environment due to seafloor characteristics. We densely sample the parameter space of the model and then use manifold learning methods to construct the surrogate model. We then validate the FIM of the surrogate model against that of the original model, which has been calculated by tediously optimizing a finite-difference approach. Finally, we present some preliminary information geometric analyses of the surrogate model.