Jul 28, 2025
Sequential Cascaded Hamiltonian Neural Networks
Ajay Mandyam Rangarajan, Jeyashree Krishnan
Understanding how neural networks can be enhanced to learn physically meaningful representations is fundamental to advancing scientific machine learning and ensuring AI safety in physics-critical applications where unpredictable model behavior can lead to catastrophic failures. We present a novel Sequential Cascaded Hamiltonian Neural Network (SC-HNN) approach that dramatically improves the generalization capabilities of standard neural networks through post-training with energy-conserving constraints. Our method consists of two stages: first training a baseline neural network on trajectory data $(x, t)$, then using automatic differentiation to extract velocities and train a separate Hamiltonian Neural Network that learns the underlying energy function. This approach requires only Hamiltonian structure knowledge (similar to standard HNNs) but operates on trajectory data rather than requiring direct access to phase space coordinates $(x, v)$. Using the harmonic oscillator as our test system, we demonstrate that this cascaded approach achieves comparable long-term stability and energy conservation to direct HNN training while significantly outperforming standalone baseline networks and PINNs. Most remarkably, we find that even when baseline neural networks fail to accurately predict long-term dynamics, their learned trajectory representations provide sufficient data fitting quality that can be leveraged to train separate Hamiltonian networks for improved generalization. The SC-HNN reduces energy variance by over 90\% compared to baseline approaches while maintaining computational efficiency. Our results suggest that standard neural networks may possess inherent physical understanding that can be recovered and enhanced through appropriate post-training procedures, opening new pathways for improving the reliability and physical consistency of learned dynamical systems without requiring physics knowledge during initial training.
Ari Brill
The project introduces and validates a novel method for training Hamiltonian neural networks involving standard neural network training as a preliminary step. The idea is interesting and the results are presented rigorously and clearly. I do have some critiques.
1) The project leans more towards AI for physics rather than physics for AI safety (however, the report does a good job discussing implications for AI safety).
2) The energy variance numbers reported in Figure 1 and Table 1 are not consistent.
3) At 8 pages + appendices, the report exceeds the page limit of 6 pages + appendices.
Oliver Klingefjord
Excellent and really thorough work!! Well presented and innovative, hats off!
Cite this work
@misc {
title={
(HckPrj) Sequential Cascaded Hamiltonian Neural Networks
},
author={
Ajay Mandyam Rangarajan, Jeyashree Krishnan
},
date={
7/28/25
},
organization={Apart Research},
note={Research submission to the research sprint hosted by Apart.},
howpublished={https://apartresearch.com}
}
