New neural ODE method discovers Lie symmetries and first integrals from data

Researchers have developed LatentLieODE, a novel neural ordinary differential equation (ODE) method capable of identifying linear Lie symmetries and first integrals from observed time-series data, such as videos. This method employs an autoencoder to map trajectories into a lower-dimensional latent space, where an infinitesimal generator bank and a multilayer perceptron (MLP) are fitted to reconstruct the original time-series. The system successfully identified symmetries and conserved quantities in six benchmark systems, achieving a correlation of at least 0.978 with ground-truth values. Notably, on a sphere dataset, it recovered a non-abelian $\mathfrak{so}(3)$ symmetry, demonstrating significant progress in data-driven discovery of symmetries and offering a new approach for creating neural surrogates of dynamical systems. AI

IMPACT This method offers a new pathway for data-driven discovery of physical laws and the creation of neural surrogates for complex dynamical systems.

RANK_REASON The cluster is about a published academic paper detailing a new method for scientific discovery using machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

• harmonic oscillator
• Killing form
• LatentLieODE
• Lotka–Volterra equations
• multilayer perceptron
• pendulum
• pixel pendulum
• rotation group SO(3)
• sphere geodesics
• twin pendulums

• paper
• other

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