Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces
This work addresses the challenge of modeling complex mechanical systems with external forces for applications in physics and engineering, representing an incremental advancement in hybrid machine learning methods.
The paper tackles the problem of learning external forces in mechanical systems by introducing pseudo-Hamiltonian neural networks, which generalize Hamiltonian formulations to separate internal and external forces, particularly for state-dependent cases, and demonstrates results on forced and damped mass-spring and tank systems with improved training using a symmetric fourth-order integration scheme.
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.