Kavli Affiliate: David Spergel
| First 5 Authors: Miles Cranmer, Sam Greydanus, Stephan Hoyer, Peter Battaglia, David Spergel
| Summary:
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.
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