Lagrangian Neural Networks
This addresses the challenge of building accurate, symmetry-preserving models in physics and related domains, offering a novel method for energy-conserving neural networks, though it is incremental in extending Lagrangian mechanics to neural networks.
The paper tackled the problem of neural networks struggling to learn physical symmetries like energy conservation by proposing Lagrangian Neural Networks (LNNs), which parameterize arbitrary Lagrangians and demonstrated energy conservation on tasks such as a double pendulum and relativistic particle, outperforming baseline approaches that incurred dissipation or failed without canonical coordinates.
Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the physical sciences, they struggle to learn these symmetries. In this paper, we propose Lagrangian Neural Networks (LNNs), which can parameterize arbitrary Lagrangians using neural networks. In contrast to models that learn Hamiltonians, LNNs do not require canonical coordinates, and thus perform well in situations where canonical momenta are unknown or difficult to compute. Unlike previous approaches, our method does not restrict the functional form of learned energies and will produce energy-conserving models for a variety of tasks. We test our approach on a double pendulum and a relativistic particle, demonstrating energy conservation where a baseline approach incurs dissipation and modeling relativity without canonical coordinates where a Hamiltonian approach fails. Finally, we show how this model can be applied to graphs and continuous systems using a Lagrangian Graph Network, and demonstrate it on the 1D wave equation.