Generalized Momentum
A physical quantity in classical mechanics defined as the partial derivative of the Lagrangian with respect to a generalized velocity. Together with generalized coordinates, it describes the state of a system within the Hamiltonian framework.
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Both the training and inference of Hamiltonian neural networks (HNNs) depend on the target system's generalized momenta, and this dependence severely limits their application in real-world scenarios.
In classical mechanics, generalized momentum is defined as the partial derivative of the Lagrangian with respect to the generalized velocity.
For complex systems (such as charged particles in electromagnetic fields or nonholonomic constrained systems), the analytical form of the generalized momenta may be very complex or even impossible to write explicitly.
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Both the training and inference of Hamiltonian neural networks (HNNs) depend on the target system's generalized momenta, and this dependence severely limits their application in real-world scenarios.
50%UnverifiedIn classical mechanics, generalized momentum is defined as the partial derivative of the Lagrangian with respect to the generalized velocity.
50%UnverifiedFor complex systems (such as charged particles in electromagnetic fields or nonholonomic constrained systems), the analytical form of the generalized momenta may be very complex or even impossible to write explicitly.
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