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Symplectic Neural Networks Based on Dynamical Systems
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We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian diffeomorphisms, interpretable and have a non-vanishing gradient property. We also give a representation theory for linear systems, meaning the proposed P-SympNets can exactly parameterize any symplectic map corresponding to quadratic Hamiltonians. Extensive numerical tests demonstrate increased expressiveness and accuracy -- often several orders of magnitude better -- for lower training cost over existing architectures. Lastly, we show how to perform symbolic Hamiltonian regression with SympNets for polynomial systems using backward error analysis.
Forward citations
Cited by 3 Pith papers
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CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts
Lifting non-conservative, actuated, and contact-constrained robot dynamics into an exactly symplectic phase-space map yields state-of-the-art out-of-distribution autoregressive rollout error at low parameter and FLOP cost.
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Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics
A discrete forced Lagrangian neural network learns conservative and dissipative dynamics from position data alone and produces structure-preserving rollouts.
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Chaoticus: a parallel approach to the computation of chaos indicators
Chaoticus is a Python package that moves chaos indicator computations (SALI, GALI, Lagrangian descriptors, Lyapunov exponents) onto GPUs and claims order-of-magnitude speedups.
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