Learning the Dynamics of the N-Body Problem through Deep Neural Networks: A Data-Driven Approach for Predictive Modeling
Keywords:
Artificial Neural Networks (ANNs), Deep learning, Deep Neural Networks (DNNs), Dynamical systems, Machine learning, n-body problemAbstract
The n-body problem, a cornerstone in classical mechanics, presents significant challenges due to its chaotic nature and lack of a general analytical solution. This paper explores a novel approach to understanding the complex gravitational dynamics of n interacting bodies by leveraging Deep Neural Networks (DNNs) as universal approximators. Unlike traditional numerical methods that iteratively solve for intermediate states, we propose a method that learns a direct mapping from initial conditions to future states, enabling one-shot predictions of positions and velocities at any given time. Our approach uses a deep learning architecture, trained on a variety of randomly sampled initial conditions, to model the evolution of the system over time. We demonstrate the capability of this model to predict the trajectories of multiple bodies with high accuracy, surpassing traditional solvers in computational efficiency, particularly in long-term predictions. By analyzing the learned models, we gain new insights into the underlying dynamics of the n-body problem, including the identification of eigenstates and stable orbits that emerge from the system’s chaotic behavior. This work marks a significant step toward integrating machine learning with classical mechanics, offering a potential paradigm shift in the numerical simulation of complex dynamical systems.
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