Symplectic Recurrent Neural Networks
Zhengdao Chen, Jianyu Zhang, Martín Arjovsky, Léon Bottou
2020International Conference on Learning Representations54 citations
Abstract
We propose Symplectic Recurrent Neural Networks (SRNNs) as learning algorithms that capture the dynamics of physical systems from observed trajectories. SRNNs model the Hamiltonian function of the system by a neural networks, and leverage symplectic integration, multiple-step training and initial state optimization to address the challenging numerical issues associated with Hamiltonian systems. We show SRNNs succeed reliably on complex and noisy Hamiltonian systems. Finally, we show how to augment the SRNN integration scheme in order to handle stiff dynamical systems such as bouncing billiards.
Topics & Concepts
Symplectic geometrySymplectic integratorLeverage (statistics)Artificial neural networkHamiltonian systemComputer scienceHamiltonian mechanicsHamiltonian (control theory)Recurrent neural networkDynamical systems theoryArtificial intelligenceApplied mathematicsMathematicsMathematical optimizationSymplectic manifoldPhysicsPure mathematicsMathematical analysisQuantum mechanicsPhase spaceModel Reduction and Neural NetworksComputational Physics and Python ApplicationsNumerical methods for differential equations