Extending the Manifold Boundary Approximation Method to reduce large-scale, multi-parameter models

The Manifold Boundary Approximation Method (MBAM) is a model reduction technique based on information geometry and sloppy model analysis. This approach interprets a multi-parameter model as a manifold with parameters as coordinates. The Fisher Information Matrix is a natural metric on this manifold, so that distance is statistical distinguishability from data. Multi-parameter models often exhibit a systematic compression of the parameter space in the information metric, so the model manifold is very narrow in most directions, a phenomenon known as sloppiness. We empirically observe that the boundaries of these manifolds are physically interpretable, reduced-order models. MBAM identifies reduced-order models using geodesics to connect a complicated model to a simpler one on the boundary. This approach is computationally and manually intensive, limiting it to moderately-sized models with a few dozen parameters. I present a computationally efficient generalization of MBAM, applicable to models with many more parameters. After reparameterizing, I recast the model reduction problem as a sequence of convex optimizations that can be solved efficiently for high-dimensional parameter spaces. I demonstrate on models from physics, biology, and power systems.