Information geometry approach to model reduction

Abstract

Information geometry combines the fields of information theory and differential geometry. In information geometry, a model is interpreted as a Riemannian manifold, referred to as the model manifold, where distance on the model manifold corresponds to statistical distinguishability. Boundaries on the model manifold are reduced-order models where a parameter or parameter combination is taken to an extreme limit and drops out of the model. Therefore, by locating the model manifold boundaries, simpler models with fewer parameters can be obtained. A model reduction algorithm which exploits this insight is the Manifold Boundary Approximation Method, or MBAM, which locates manifold boundaries by calculating geodesics on the surface of the model manifold. This can be done iteratively to find increasingly simple reduced models. We demonstrate this method for model reduction using the Pekeris waveguide transmission loss model. A machine learned surrogate model for the Pekeris waveguide is constructed so that the necessary derivatives for calculating geodesics can be easily obtained using automatic differentiation. [Work supported by the Office of Naval research Grant N00014-21-S-B001.]