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.