Paper ID: 2410.20951 • Published Oct 28, 2024
Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?
Tae-Geun Kim, Seong Chan Park
TL;DR
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We propose a novel framework based on neural network that reformulates
classical mechanics as an operator learning problem. A machine directly maps a
potential function to its corresponding trajectory in phase space without
solving the Hamilton equations. Most notably, while conventional methods tend
to accumulate errors over time through iterative time integration, our approach
prevents error propagation. Two newly developed neural network architectures,
namely VaRONet and MambONet, are introduced to adapt the Variational LSTM
sequence-to-sequence model and leverage the Mamba model for efficient temporal
dynamics processing. We tested our approach with various 1D physics problems:
harmonic oscillation, double-well potentials, Morse potential, and other
potential models outside the training data. Compared to traditional numerical
methods based on the fourth-order Runge-Kutta (RK4) algorithm, our model
demonstrates improved computational efficiency and accuracy.
Code is available at: this https URL