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Learning Integrable Dynamics with Action-Angle Networks
Ameya Daigavane · Arthur Kosmala · Miles Cranmer · Tess Smidt · Shirley Ho

Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned simulators typically predict the evolution of the system in a step-by-step manner with numerical integration techniques. However, such models often suffer from instability over long roll-outs due to the accumulation of both estimation and integration error at each prediction step. Here, we propose an alternative construction for learned physical simulators that are inspired by the concept of action-angle coordinates from classical mechanics for describing integrable systems. We propose Action-Angle Networks, which learn a nonlinear transformation from input coordinates to the action-angle space, where evolution of the system is linear. Unlike traditional learned simulators, Action-Angle Networks do not employ any higher-order numerical integration methods, making them extremely efficient at modelling the dynamics of integrable physical systems.

Author Information

Ameya Daigavane (Massachusetts Institute of Technology)
Arthur Kosmala (Ludwig-Maximilians-Universität München)
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.

Tess Smidt (Massachusetts Institute of Technology)
Shirley Ho (Flatiron Institute)

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.

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