| Abstract: |
| We present a neural network architecture capable of learning the parameter-dependent flow of a Hamiltonian system subject to external forcing, while preserving the underlying Lagrange-d`Alembert structure. We demonstrate that this architecture can learn the flows of time-dependent systems---both deterministic and stochastic---and more accurately emulate the system`s energy evolution compared to general-purpose, non-structure-preserving neural networks. This results in more stable and higher-quality solutions. We also discuss prospective applications to structure-preserving model reduction of stochastic Hamiltonian systems. |
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