Re-Hamiltonian Generative Networks

Carles Balsells Rodas, Oleguer Canal, Federico Taschin

Keywords: Hamiltonian, Generative, Artificial Neural Network, Machine Learning

Abstract:

Scope of Reproducibility:
The main objective of the paper is to "learn the Hamiltonian dynamics of simple physical systems from high-dimensional observations without restrictive domain assumptions". To do so, the authors train a generative model that reconstructs an inputted sequence of images of the evolution of some physical system. For instance, they learn the dynamics of a pendulum, a body-spring system, and 2,3-bodies. In addition to these environments, we further expand the testing on two new environments and we explore architecture tweaks looking for performance gains.

Methodology:
We implement the project with Python using Pytorch as a deep learning library. Previous to ours, there was no public implementation of this work. Thus, we had to write the code of the simulated environments, the deep models, and the training process. The code can be found in this repository: https://github.com/CampusAI/Hamiltonian-Generative-Networks. A single training takes around 4 hours and 1910MB of GPU memory (NVIDIA GeForce RTX2080Ti).

Results:
We found the model's input-output data slightly unclear in the original paper. First, it seems that the model reconstructs the exact same sequence that has been inputted. Nevertheless, further discussion with the authors seems to indicate that they input the first few frames to the network and reconstructed the rest of the rollout. We test both approaches and analyze the results. We generally obtain comparable results to those of the original authors when just reconstructing the input sequence (30% average absolute relative error w.r.t. to their reported values) and worse results when trying to reconstruct unseen frames (107% error). In this report, we include our intuition on possible reasons that would explain these observations.

What was easy:
The architecture of the model and training procedure was easy to understand from the paper. In addition, creating simulation environments similar to those of the original authors was also straight forward.

What was difficult:
While the overall model architecture and data generation were easy to understand, we encountered the optimization to be especially tricky to perform. In particular, finding a good balance between the reconstruction loss and KL divergence loss was challenging. We implemented GECO algorithm to dynamically adapt the Lagrange multiplier but it proved to be surprisingly brittle to its hyper-parameters, resulting in very unstable behavior. We were unable to identify the cause of the problem and ended up training with simpler techniques such as using a fixed Lagrange multiplier as presented in the beta-VAE paper.

Communication with original authors:
We exchanged around 6 emails with doubts and answers with the original authors.

Paper Url: https://openreview.net/forum?id=w23q3ttruo&noteId=XenPH-P3an