affect conclusions. They may also aid science communication and education for
policy makers and the general public.

The situation in climate is reminiscent of that in power systems that
similarly use multi-physics to model large engineered systems. When complex
models fail to match data (even presumably identified models), for example in
well-instrumented blackouts [132], it is bewildering to identify the source of
the problem. Simplified models make it easier to identify and correct errors
in the model. Our model reduction methods have made inroads towards this end
in power systems [32]; can they similarly find use in these other areas?

Power systems application also face the challenge that they operate at the
intersection of industry and government where issues of individual privacy,
proprietary information, and public security are relevant. Model reduction is
a means to limit and regulate how information is shared or redacted among
vested parties. Models that contain sensitive infrastructure information can
be systematically and objectively coarse-grained to remove classified pieces
while simultaneously meeting the demands of public disclosure and oversight.

The computational cost of solving the geodesic equation limit the scope of
current algorithms to models with at most a few hundred parameters, so
alternative strategies are needed. It may be possible to guide optimization
algorithms toward the boundary; merging the fitting and reduction steps.
Alternative approaches may focus on targeted subsets of parameters. The
topological relationship among potential models remains largely unexplored,
but such a theory could better inform model selection for target applications.

###  8.5 Conclusions

Efficiently reasoning with big models and big data will require new
organizational paradigms [133, 134]. The physical theories of the twentieth
century, interconnected through a web of classical limits as in Figure 8,
suggest a way forward. Effective theories organize our understanding and focus
our attention to the relevant physical principles within specific regimes of
validity. The hyperribbons presented here reflect a similar information
hierarchy, but sloppiness adds a new wrinkle to the traditional narrative by
justifying simple theories without resorting to classical limits, coarse-
graining, or renormalization. Visualization tools and model reduction methods
extract simple explanations in a context-specific way, and our theories of
information topology organize them into a network of interrelated models, each
applicable at an appropriate scale and for specific applications. While
science has traditionally progressed by discovering effective theories before
the underlying mechanism, the future of science may well operate in the
opposite direction, cataloging and organizing effective theories for the
universe’s myriad complexities. Sloppy models abetted with the formalism of
information geometry explain why and how this can be done.

## Acknowledgments

We would like to thank David Schwab and Pratik Chaudhari for helpful
conversations. KNQ was supported in part by the US National Science
Foundation, through the Center for the Physics of Biological Function
(PHY-1734030) and from NSF DMR-1719490. Parts of this work were performed at
the Aspen Center for Physics, supported by NSF grant PHY-1607611. The
participation of MCA at Aspen was supported by the Simons Foundation. MKT was
supported by NSF EPCN-1710727, NSF CMMT-1753357, and NSF CMMT-1834332. JPS was
supported by NSF DMR-1719490. BBM and MCA were supported by a Simons
Investigator award, and BBM was supported by NIH R35 GM138341

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