Lagrangian Neural Networks

By Miles Cranmer, Sam Greydanus, Stephan Hoyer, Peter W. Battaglia, David N. Spergel, Shirley Ho. International Conference on Learning Representations, 2020

615 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1926103a9a5c9099b42652c0192b5fcda571d36f

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In Artificial Intelligence

In Statistical and Nonlinear Physics

Citations in the corpus

Discovering Symbolic Models from Deep Learning with Inductive Biases (2020, methodology): “This is a Hamiltonian version of the Lagrangian Graph Network in [47], and is similar to [48].”
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, background): “Other studies have investigated the similarities of dynamical systems and deep learning methods [65] and employed conservation laws to learn systems described by Hamiltonian mechanics [18, 12].”
Characterizing possible failure modes in physics-informed neural networks (2021, background): “Some approaches have focused on embedding specialized physical constraints into NNs, such as conservation of energy or momentum [4, 12] or multiscale features [34].”
Continuous-in-Depth Neural Networks (2020, background): “Due to their popularity, there is a rich body of work that aims to explain “why” shortcut connections between layers enables the training of very deep NNs [73, 4, 29, 48, 51, 44].”