Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learning
Authors: Yeongwoo Song, Hawoong Jeong
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate that the meta-trained model captures the generalized Hamiltonian representation that is consistent across different physical domains. Overall, through the use of meta learning, we offer a framework that achieves cross domain generalization, providing a step towards a unified model for understanding a wide array of dynamical systems via deep learning. |
| Researcher Affiliation | Academia | Yeongwoo Song1 Hawoong Jeong1 2 1Department of Physics, KAIST 2Center for Complex Systems, KAIST ywsong1025@kaist.ac.kr, hjeong@kaist.edu |
| Pseudocode | No | The paper does not contain any section or figure explicitly labeled as "Pseudocode" or "Algorithm". |
| Open Source Code | No | The paper does not include any explicit statement or link indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | For all of our systems, we generated a dataset with N = 10, 000 trajectories confined to the two-dimensional space... We provide the detailed procedure for generating the dataset in the SM A.2. |
| Dataset Splits | Yes | We evaluate the performance by making a few-step gradient descent on the unseen type of system during the meta training phase with K = 50 data points. ... For both meta-training and pre-training, we used a learning rate of α = 0.001 for the gradient step on the inner loop, and the Adam optimizer on the outer loop with a learning rate of β = 0.0005. The inner gradient update was 1 step, with a total of 5000 iterations on the outer loop. The number of task batches is set to 10, and the number of phase points used for each task was 50 (i.e. among the 200 points in each trajectory, 50 points were randomly sampled for meta training). |
| Hardware Specification | Yes | We perform our experiments on NVIDIA RTX A6000 by performing 10 independent runs as default to ensure the stability of our results and report the average and standard error values. |
| Software Dependencies | Yes | Using the Hamiltonian described in Section 3.1, we obtained the state trajectories (q, p) by employing the LSODA integrator implemented in Sci Py (Virtanen et al., 2020). |
| Experiment Setup | Yes | Our model is composed of three GCN layers to extract features of the input states, preceded by three fully connected linear layers for the regression of Hamiltonian value. We choose the mish function as the non-linear activation function. ... For both meta-training and pre-training, we used a learning rate of α = 0.001 for the gradient step on the inner loop, and the Adam optimizer on the outer loop with a learning rate of β = 0.0005. The inner gradient update was 1 step, with a total of 5000 iterations on the outer loop. The number of task batches is set to 10, and the number of phase points used for each task was 50. |