Pseudo-Hamiltonian neural networks with state-dependent external forces

• Published in: Physica. D Vol. 446; p. 133673
• Main Authors: Eidnes, Sølve, Stasik, Alexander J., Sterud, Camilla, Bøhn, Eivind, Riemer-Sørensen, Signe
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2023
• Subjects: Hybrid machine learning; Physics-informed machine learning; Pseudo-Hamiltonian neural networks; Physics-informed machine learning; Pseudo-Hamiltonian neural networks; Hybrid machine learning
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2023.133673

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. •We present pseudo-Hamiltonian neural networks with state-dependent external forces.•The method is tested for a mass–spring system and a system of tanks and pipes.•The method can be used to learn disturbances on a system, e.g. detection of leaks.•Models learned on a disturbed system can predict future states without disturbances.•A fourth-order symmetric integrator is introduced and outperforms standard methods.