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Equivariant and Modular DeepSets with Applications in Cluster Cosmology
Leander Thiele · Miles Cranmer · Shirley Ho · David Spergel

We design modular and rotationally equivariant DeepSets for predicting a continuous background quantity from a set of known foreground particles. Using this architecture, we address a crucial problem in Cosmology: modelling the continuous electron pressure field inside massive structures known as “clusters.” Given a simulation of pressureless, dark matter particles, our networks can directly and accurately predict the background electron pressure field. The modular design of our architecture makes it possible to physically interpret the individual components. Our most powerful deterministic model improves by 70% on the benchmark. A conditional-VAE extension yields further improvement by 7%, being limited by our small training set however. We envision use cases beyond theoretical cosmology, for example in soft condensed matter physics, or meteorology and climate science.

Author Information

Leander Thiele (Princeton University)
Miles Cranmer (Princeton University)

Miles Cranmer is an Astro PhD candidate trying to accelerate astrophysics with AI. Miles is from Canada and did his undergraduate in Physics at McGill. He is deeply interested in the automation of science, particularly aspects that are not yet tractable with existing machine learning, such as experiment planning, simulation, and theory. He works on symbolic regression, graph neural networks, normalizing flows, and learned simulation. He is hugely interested in symbolic ML, since, as he argues, symbolic models seem to be a surprisingly efficient basis for describing our universe.

Shirley Ho (Flatiron institute/ New York University/ Carnegie Mellon)

Shirley Ho is a group leader and acting director at Flatiron Institute at Simons foundation, a research professor of physics and an affiliated faculty at Center for Data Science at NYU. Ho also holds associate (adjunct) professorship at Carnegie Mellon University and visiting appointment at Princeton University. She was a senior scientist at Berkeley National Lab from 2016-2018 and a Cooper-Siegel Development chair professor at Carnegie Mellon University before that. Ho was a Seaborg and Chamberlain Fellow from 2008-2011 at Berkeley Lab, after receiving her PhD in Astrophysics from Princeton University in 2008 under supervision of David Spergel. Ho graduated summa cum laude with a B.A. in Physics and a B.A. in Computer Science from UC Berkeley. A cited expert in cosmology, machine learning applications in astrophysics and data science,her interests are using deep learning accelerated simulations to understand the Universe, and other astrophysical phenomena. She tries her best to balance her love for the Universe, the machine and life especially during these crazy times.

David Spergel (Flatiron Institute)

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