Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces

Abstract

Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a generalization of the Hamiltonian formulation via the port-Hamiltonian formulation, and show that pseudo-Hamiltonian neural network models can be used to learn external forces acting on a system. We argue that this property is particularly useful when the external forces are state dependent, in which case it is the pseudo-Hamiltonian structure that facilitates the separation of internal and external forces. Numerical results are provided for a forced and damped mass-spring system and a tank system of higher complexity, and a symmetric fourth-order integration scheme is introduced for improved training on sparse and noisy data.

23 pages, 13 figures; v4: slight title change, expanded on methodology for more clarity, updated plots

References in corpus (2)

• GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems
• Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems

Cited by in corpus (1)

• Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems