Port-Hamiltonian Neural Networks with State Dependent Ports

• URL: http://arxiv.org/abs/2206.02660v1
• Date: Mon, 6 Jun 2022 14:57:25 GMT
• Title: Port-Hamiltonian Neural Networks with State Dependent Ports
• Authors: S{\o}lve Eidnes, Alexander J. Stasik, Camilla Sterud, Eivind B{\o}hn and Signe Riemer-S{\o}rensen
• Abstract summary: We stress-test the method on both simple mass-spring systems and more complex and realistic systems with several internal and external forces. Port-Hamiltonian neural networks can be extended to larger dimensions with state-dependent ports. We propose a symmetric high-order integrator for improved training on sparse and noisy data.
• Score: 58.720142291102135
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems. In this work, we stress-test the method on both simple mass-spring systems and more complex and realistic systems with several internal and external forces, including a system with multiple connected tanks. We quantify performance under various conditions and show that imposing different assumptions greatly affect the performance during training presenting advantages and limitations of the method. We demonstrate that port-Hamiltonian neural networks can be extended to larger dimensions with state-dependent ports. We consider learning on systems with known and unknown external forces and show how it can be used to detect deviations in a system and still provide a valid model when the deviations are removed. Finally, we propose a symmetric high-order integrator for improved training on sparse and noisy data.

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