Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints
Authors: Marc Finzi, Ke Alexander Wang, Andrew G. Wilson
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our experiments show that Cartesian coordinates with explicit constraints lead to a 100x improvement in accuracy and data efficiency. |
| Researcher Affiliation | Academia | Marc Finzi New York University Ke Alexander Wang Cornell University Andrew Gordon Wilson New York University |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Code for our experiments can be found at: https://github.com/mfinzi/constrained-hamiltonian-neural-networks. |
| Open Datasets | No | Appendix E describes each system in detail and explains our data generation procedure. No explicit link, DOI, or formal citation is provided for public access to the generated datasets. |
| Dataset Splits | No | No explicit mention of training/validation/test dataset splits with percentages, sample counts, or specific predefined split citations. It mentions 'Ntest = 100 initial conditions from the test set' but not the training or validation splits. |
| Hardware Specification | No | No specific hardware details (like GPU/CPU models, memory, or cloud instance types) are mentioned for running experiments. |
| Software Dependencies | No | No specific software dependencies with version numbers (e.g., 'Python 3.8, PyTorch 1.9') are explicitly stated in the paper. |
| Experiment Setup | Yes | For each trajectory, we compute the L1 loss averaged over each timestep of the trajectory7 L(z, ˆz) = 1 n Pn i=1 ˆzi zi 1 and compute gradients by differentiating through ODESolve directly. We use n = 4 timesteps for our training trajectories and average L(z, ˆz) over a minibatch of size 200. To ensure a fair comparison, we first tune all models and then train them for 2000 epochs which was sufficient for all models to converge. For more details on training and settings, see Appendix D.2. |