Discovering conservation laws from trajectories via machine learning
This work addresses the challenge of automatically discovering conservation laws from large-scale data, which is a fundamental problem in physics and engineering, benefiting researchers and practitioners analyzing complex dynamical systems.
This paper introduces ConservNet, a neural network designed to discover conserved quantities from grouped trajectory data. It successfully identifies underlying invariants in simulated systems and a real-world double pendulum trajectory, demonstrating robustness to noise and various data conditions.
Invariants and conservation laws convey critical information about the underlying dynamics of a system, yet it is generally infeasible to find them from large-scale data without any prior knowledge or human insight. We propose ConservNet to achieve this goal, a neural network that spontaneously discovers a conserved quantity from grouped data where the members of each group share invariants, similar to a general experimental setting where trajectories from different trials are observed. As a neural network trained with a novel and intuitive loss function called noise-variance loss, ConservNet learns the hidden invariants in each group of multi-dimensional observables in a data-driven, end-to-end manner. Our model successfully discovers underlying invariants from the simulated systems having invariants as well as a real-world double pendulum trajectory. Since the model is robust to various noises and data conditions compared to baseline, our approach is directly applicable to experimental data for discovering hidden conservation laws and further, general relationships between variables.