# Port-Hamiltonian Approach to Neural Network Training

arXiv: https://arxiv.org/abs/1909.02702 · HTML: https://mlsanity.com/paper/1909.02702/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [Optimal Energy Shaping via Neural Approximators](https://mlsanity.com/paper/2101.05537/) (2021)
- [Can we learn gradients by Hamiltonian Neural Networks?](https://mlsanity.com/paper/2111.00565/) (2021)
- [Who breaks early, looses: goal oriented training of deep neural networks based on port Hamiltonian dynamics](https://mlsanity.com/paper/2304.07070/) (2023)

## Abstract (arXiv)

Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but are solutions of an ordinary differential equation (ODE); however, these networks are still optimized via discrete methods (e.g. gradient descent). In this paper, we explore a different direction: namely, we propose a novel framework for learning in which the parameters themselves 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. Numerical experiments have been performed to show the validity and effectiveness of the proposed methods.