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Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Control

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Document pages: 17 pages

Abstract: Recent approaches for modelling dynamics of physical systems with neuralnetworks enforce Lagrangian or Hamiltonian structure to improve prediction andgeneralization. However, when coordinates are embedded in high-dimensional datasuch as images, these approaches either lose interpretability or can only beapplied to one particular example. We introduce a new unsupervised neuralnetwork model that learns Lagrangian dynamics from images, withinterpretability that benefits prediction and control. The model infersLagrangian dynamics on generalized coordinates that are simultaneously learnedwith a coordinate-aware variational autoencoder (VAE). The VAE is designed toaccount for the geometry of physical systems composed of multiple rigid bodiesin the plane. By inferring interpretable Lagrangian dynamics, the model learnsphysical system properties, such as kinetic and potential energy, which enableslong-term prediction of dynamics in the image space and synthesis ofenergy-based controllers.

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