Hi, everyone! We have a guest speaker for our Seminar, and you are all cordially invited to the AMLab Seminar on Thursday 3rd December at 16:00 CET on Zoom, where Miles Cranmer will give a talk titled “LAGRANGIAN NEURAL NETWORKS”.
Title : LAGRANGIAN NEURAL NETWORKS
Abstract : 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 lagrangian 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 Hamiltonianapproach fails. Finally, we show how this model can be applied to graphs and continuous systems using a Lagrangian Graph Network, and demonstrate it on the1D wave equation.
Paper Link: https://arxiv.org/pdf/2003.04630.pdf
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