Nonseparable Symplectic Neural Networks
Authors: Shiying Xiong, Yunjin Tong, Xingzhe He, Shuqi Yang, Cheng Yang, Bo Zhu
ICLR 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrated the efficacy and versatility of our method by predicting a wide range of Hamiltonian systems, both separable and nonseparable, including chaotic vortical flows. We showed the unique computational merits of our approach to yield long-term, accurate, and robust predictions for large-scale Hamiltonian systems by rigorously enforcing symplectomorphism. |
| Researcher Affiliation | Collaboration | Shiying Xionga , Yunjin Tonga, Xingzhe Hea, Shuqi Yanga, Cheng Yangb, Bo Zhua a Dartmouth College, Hanover, NH, United States b Byte Dance AI Lab, Beijing, China |
| Pseudocode | Yes | Algorithm 1 Integrate (4) by using the second-order symplectic integrator |
| Open Source Code | No | The paper does not provide any concrete access information (e.g., specific repository link, explicit code release statement, or code in supplementary materials) for the source code of the described methodology. |
| Open Datasets | No | We generate the dataset for training and validation using high-precision numerical solver (Tao, 2016)... |
| Dataset Splits | Yes | We generate the dataset for training and validation using high-precision numerical solver (Tao, 2016), where the ratio of training and validation datasets is 9 : 1. |
| Hardware Specification | No | The paper does not specify any particular hardware components (e.g., specific GPU models, CPU models, or memory) used for running the experiments. It lacks details beyond general computing environments. |
| Software Dependencies | No | The paper mentions 'Pytorch (Paszke et al., 2019)' but does not provide a specific version number for this or any other software dependency. |
| Experiment Setup | Yes | We use 6 linear layers with hidden size 64 to model Hθ, all of which are followed by a Sigmoid activation function except the last one... The weights of the linear layers are initialized by Xavier initializaiton... We set the time span, time step and dateset size as T = 0.01, dt = 0.01 and Ns = 1280... We set ω = 2000... We pick the L1 loss function to train our network... We use the Adam optimizer (Kingma & Ba, 2015) with learning rate 0.05. The learning rate is multiplied by 0.8 for every 10 epoches. |