Newton vs the machine: solving the chaotic three-body problem using deep neural networks
arXiv:1910.07291 · doi:10.1093/mnras/staa713
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 solutions 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 fixed computational cost and up to 100 million times faster than a state-of-the-art solver. 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.
arXiv comment6 pages, 6 figures
References in corpus (11)
- TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems
- Black hole mergers in the universe
- Multi-physics simulations using a hierarchical interchangeable software interface
- Dynamical evolution of black hole sub-systems in idealised star clusters
- Black Hole Mergers From Globular Clusters Observable by LISA I: Eccentric Sources Originating From Relativistic -body Dynamics
- Probabilistic Numerics and Uncertainty in Computations
- A Statistical Solution to the Chaotic, Non-Hierarchical Three-Body Problem
- On black hole sub-systems in idealized nuclear star clusters
- Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length
- Numerical verification of the microscopic time reversibility of Newton's equations of motion: Fighting exponential divergence
- Enforcing constraints for time series prediction in supervised, unsupervised and reinforcement learning
Cited by in corpus (31)
- Review: Deep Learning in Electron Microscopy
- Physics enhanced neural networks predict order and chaos
- On the risks of using double precision in numerical simulations of spatio-temporal chaos
- Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
- Fast emulation of quantum three-body scattering
- Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE
- Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithm
- Estimating the outcomes of common envelope evolution in triple stellar systems
- Hypersolvers: Toward Fast Continuous-Depth Models
- A neural network-based methodology to select young stellar object candidates from IR surveys
- Artificial Intelligence, Chaos, Prediction and Understanding in Science
- Depth-Width Trade-offs for ReLU Networks via Sharkovsky's Theorem
- Sparse Symplectically Integrated Neural Networks
- Machine learning prediction for mean motion resonance behaviour -- The planar case
- Black Hole Weather Forecasting with Deep Learning: A Pilot Study
- A hybrid approach for solving the gravitational N-body problem with Artificial Neural Networks
- How neural networks learn to classify chaotic time series
- Modeling the Time Evolution of Compact Binary Systems with Machine Learning
- Introducing a new multi-particle collision method for the evolution of dense stellar systems. Crash-test N-body simulations
- On Computational Poisson Geometry II: Numerical Methods
- Controlling Neural Networks with Rule Representations
- Large-step neural network for learning the symplectic evolution from partitioned data
- Adaptive Techniques in Practical Quantum Key Distribution
- Differential Euler: Designing a Neural Network approximator to solve the Chaotic Three Body Problem
- Rydberg excitons in cuprous oxide: A two-particle system with classical chaos
- Neural Physicist: Learning Physical Dynamics from Image Sequences
- On the space-time expressivity of ResNets
- Data-Driven Time Propagation of Quantum Systems with Neural Networks
- Advanced Techniques in Stability Analysis of Trans-Neptunian Objects
- Data-Driven Continuum Dynamics via Transport-Teleport Duality
- Clustering and enhanced classification using a hybrid quantum autoencoder