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Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control
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In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate inductive bias by designing the associated computation graph in a physics-informed manner. In particular, we enforce Hamiltonian dynamics with control to learn the underlying dynamics in a transparent way, which can then be leveraged to draw insight about relevant physical aspects of the system, such as mass and potential energy. In addition, we propose a parametrization which can enforce this Hamiltonian formalism even when the generalized coordinate data is embedded in a high-dimensional space or we can only access velocity data instead of generalized momentum. This framework, by offering interpretable, physically-consistent models for physical systems, opens up new possibilities for synthesizing model-based control strategies.
Forward citations
Cited by 4 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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Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity
Q-pHNNs learn classical conservative and dissipative dynamics by mapping the port-Hamiltonian J matrix to unitary gates and the R matrix to mid-circuit measurement nonlinearity, enforcing structure by construction.
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Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network
SGFNN learns a stochastic generating function via an autoencoder from paired state observations, yielding symplectic and more accurate long-term predictions for stochastic Hamiltonian systems than sFML.
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Weight-Parameterization in Continuous Time Deep Neural Networks for Surrogate Modeling
Legendre-polynomial weight parameterization lowers training cost and improves stability in continuous-time network surrogates, but the reported accuracy advantage conflicts with the paper's own error table.
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