Learning Deterministic and Stochastic Forced Hamiltonian Systems
We develop a geometric framework for learning deterministic and stochastic forced Hamiltonian systems with neural networks. Motivated by the Lagrange-d'Alembert principle and the theory of variational integrators, we introduce the notion of a Lagrange-d'Alembert map and establish a $C^r$ convergence theorem for first-order one-step methods. Building on these results, we propose Generalized Forced Hamiltonian Neural Networks (GFHNNs), a class of structure-preserving neural networks obtained by concatenating Lagrange-d'Alembert-Euler maps, and prove a universal approximation theorem for this architecture. We further extend the framework to parameter-dependent systems, leading to Parametric ...
| Authors | Benedikt Brantner, Tomasz Tyranowski |
|---|---|
| Primary category | math.NA |
| Published | 20 August 2026 |
| Last updated at source | 20 August 2026 |
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