Deep Energy-based Modeling of Discrete-Time Physics
Authors: Takashi Matsubara, Ai Ishikawa, Takaharu Yaguchi
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 4 Learning of Partial and Ordinary Differential Equations Comparative Models. We examined the proposed DGNet and comparative methods. |
| Researcher Affiliation | Academia | Takashi Matsubara Osaka University Osaka, Japan 560 8531 matsubara@sys.es.osaka-u.ac.jp Ai Ishikawa Kobe University Kobe, Japan 657 8501 a-ishikawa@stu.kobe-u.ac.jp Takaharu Yaguchi Kobe University Kobe, Japan 657 8501 yaguchi@pearl.kobe-u.ac.jp |
| Pseudocode | Yes | For reference, we introduce the case with a neural network that is composed of a chain of functions in Algorithm 1 in Appendix F. |
| Open Source Code | Yes | The proposed algorithm can be implemented in a similar way to the current automatic differentiation algorithm [20]; we provide it as a Py Torch library [31]1. 1https://github.com/tksmatsubara/discrete-autograd |
| Open Datasets | Yes | We employed Hamiltonian systems that were examined in the original study of the HNN [19], namely a mass-spring system, a pendulum system, and a 2-body system... We evaluated the models on the real pendulum dataset that were obtained by Schmidt and Lipson [39] following the study on the HNN [19]... We simulated the equation with a time step size of t = 0.001 for 500 steps and obtained 100 time series (90 for training and 10 for the test). |
| Dataset Splits | No | For the Kd V equation and Cahn Hilliard equation datasets, the paper states 'obtained 100 time series (90 for training and 10 for the test)' without mentioning a validation split. For other datasets, no explicit split information is provided beyond being used for training and test. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory) used for running its experiments. It only discusses the computational cost qualitatively. |
| Software Dependencies | No | The paper mentions implementation as a 'Py Torch library' and uses the 'Adam optimizer', but it does not specify explicit version numbers for these software dependencies, only providing a citation for PyTorch. |
| Experiment Setup | Yes | Each network was trained using the Adam optimizer [25] with a batch size of 200 and a learning rate of 0.001 for 10,000 iterations... We employed a neural network composed of a 1-dimensional convolution layer followed by two fully-connected layers. A convolution layer with a kernel size of 3 is enough to learn the central difference. The matrix G = D was implemented as a 1-dimensional convolution layer with the kernel of ( 1/2 x, 0, 1/2 x) and periodic padding. Following the study on the HNN [19], the activation function was the hyperbolic tangent, the number of hidden channels was 200, and each weight matrix was initialized as a random orthogonal matrix. |