Newton versus the machine: solving the chaotic three-body problem using deep neural networks

Journal Article · Wed Apr 22 00:00:00 EDT 2020 · Monthly Notices of the Royal Astronomical Society

DOI:https://doi.org/10.1093/mnras/staa713· OSTI ID:1615692

Breen, Philip G. ^[1]; Foley, Christopher N. ^[2]; Boekholt, Tjarda ^[3]; Zwart, Simon Portegies ^[4]

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1. School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Kings Buildings, Edinburgh EH9 3JZ, UK, Roar AI, 3rd Floor, 116 Dundas Street, Edinburgh EH3 5DQ, UK
2. School of Clinical Medicine, University of Cambridge, Cambridge, CB2 0SP, UK
3. CIDMA, Departamento de Física, Universidade de Aveiro, Campus de Santiago, P-3810-193 Aveiro, Portugal
4. Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands

ABSTRACT Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be found by performing laborious iterative calculations that have unpredictable and potentially infinite computational cost, due to the system’s chaotic nature. We show that an ensemble of converged solutions for the planar chaotic three-body problem obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (ANN) that, over a bounded time interval, provides accurate solutions at a fixed computational cost and up to 100 million times faster than the numerical integrator. In addition, we demonstrate the importance of training an ANN using converged solutions from an arbitrary precise integrator, relative to solutions computed by a conventional fixed precision integrator, which can introduce errors in the training data, due to numerical round-off and time discretization, that are learned by the ANN. Our results provide evidence that, for computationally challenging regions of phase space, a trained ANN can replace existing numerical solvers, enabling fast and scalable simulations of many-body systems to shed light on outstanding phenomena such as the formation of black hole binary systems or the origin of the core collapse in dense star clusters.

• Sponsoring Organization: USDOE Office of Energy Efficiency and Renewable Energy (EERE), Transportation Office. Fuel Cell Technologies Office
• Grant/Contract Number: UID/MAT/04106/2019; SFRH/BPD/122325/2016
• OSTI ID: 1615692
• Journal Information: Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Vol. 494 Journal Issue: 2; ISSN 0035-8711
• Publisher: Oxford University Press
• Country of Publication: United Kingdom
• Language: English