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Understanding the physics of the deep solar interior, and the more exotic environs of core-collapse supernovae (CCSN) and binary neutron-star (NS) mergers, is of keen interest in many avenues of research. To date, this physics is based largely on simulations via forward integration. While these simulations provide valuable constraints, it could be insightful to adopt the “inverse approach” as a point of comparison. Within this paradigm, parameters of the solar interior are not output based on an assumed model, but rather are inferred based on real data.We take the specific case of solar electron number density, which historically is taken as output from the standard solar model. We show how one may arrive at an independent constraint on that density profile based on available neutrino flavor data from the Earth-based Borexino experiment. The inference technique’s ability to offer a unique lens on physics can be extended to other datasets, and to analogous questions for CCSN and NS mergers, albeit with simulated data. 

Inference is a term that encompasses many techniques including statistical data assimilation (SDA). Unlike machine learning, which is designed to harness predictive power from extremely large data sets, SDA is designed for sparsely-sampled systems. This is the realm of study of nonlinear dynamical systems in nature. Formulated as an optimization procedure, SDA can be considered a path-integral approach to state and parameter estimation. Within this formulation, we can use the physical principle of least action to identify optimal solutions: solutions that are consistent with both measurements and a dynamical model assumed to give rise to those measurements. I review examples from neurobiology and an epidemiological model tailored to the coronavirus SARS-CoV-2, to demonstrate the versatility of SDA across the sciences, and how these distinct applications possess commonalities that can inform one another.