Information geometry for environmental inversions in ocean acoustics

Environmental inversions in ocean acoustics require the simultaneous estimation of many unknown parameters. Broad studies of multi-parameter models from diverse fields have shown that such inference problems are universally sloppy. Sloppiness is a phenomenon in which the predictions of a model are insensitive to all but a few key combinations of parameters. Sloppy model analysis is based on information geometry, an application of differential geometry to statistics. In this talk, we give an overview of information geometry for underwater acoustics models for environmental inversion, focusing on transmission loss (TL) in range-independent normal mode models. We demonstrate that these models are sloppy and how the geometry directly relates the information content of acoustic data to the relevance of environmental parameters. In particular, the model manifold quantifies what environmental information is encoded in ocean sounds and how unidentifiable parameters can be removed from the model to give a simplified, identifiable ocean acoustics model of comparable accuracy. We summarize physical insights revealed by this information geometry analysis for ocean inversion. [Work supported by Office of Naval Research]