A new framework for learning in which the neural network parameters are solutions of ODEs. By viewing the optimization process as the evolution of a port-Hamiltonian system we can ensure convergence to a minimum of the objective function.
This method is applicable to any generic neural network architecture. The neural network is coupled to a fictitious Port-Hamiltonian system whose states are given by the neural network parameters. The energy of the Port-Hamiltonian system is then linked to the objective function and automatically minimized due to the PH passivity property.
Code for "Port-Hamiltonian Approach to Neural Network Training" to appear in the 58th IEEE Conference on Decision and Control (CDC 2019). arXiv preprint available here.
pyPH/numpy_simple.py contains a numpy implementation of a single linear predictor along with functions that describe the Port-Hamiltonian ODE of its parameters. For general use import the PHNN class in pyPH/model.py instead.
pyPH/phnn.py contains the new optimizer class proposed in the paper. The class take as input PyTorch torch.nn.Modules and provides a fit method to optimize them as Port-Hamiltonian Neural Networks.