FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities
Authors: Takashi Matsubara, Takaharu Yaguchi
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluated FINDE and base models using datasets associated with first integrals; these are summarized in Table 2. A gravitational two-body problem (2-body) on a 2-dimensional configuration space is a typical Hamiltonian system in the canonical form. In addition to the total energy, the system has first integrals related to symmetries in space, namely, the linear and angular momenta. |
| Researcher Affiliation | Academia | Takashi Matsubara Osaka University Toyonaka, Osaka, 560 8531 Japan matsubara@sys.es.osaka-u.ac.jp Takaharu Yaguchi Kobe University Kobe, Hyogo, 657 8501 Japan yaguchi@pearl.kobe-u.ac.jp |
| Pseudocode | No | The paper does not contain pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | Yes | We implemented all codes by modifying the officially released codes of HNN (Greydanus et al., 2019) 1 and DGNet (Matsubara et al., 2020)2. ... The authors have enclosed the source code for generating the datasets and running the experiments as supplementary material. |
| Open Datasets | Yes | We generated a time-series set of each dataset with different initial conditions (hence, different values of first integrals). See Appendix C for more details. ... The authors have enclosed the source code for generating the datasets and running the experiments as supplementary material. |
| Dataset Splits | No | The paper specifies the number of time-series for 'training' and 'evaluation' (testing) but does not mention specific percentages or counts for a separate validation split. |
| Hardware Specification | Yes | All experiments were performed on a single NVIDIA A100. |
| Software Dependencies | Yes | We used Python v. 3.8.12 with packages scipy v. 1.7.3, pytorch v. 1.10.2, torchdiffeq v. 0.1.1, functorch v. 1.10 preview, and gplearn v. 0.4.2. |
| Experiment Setup | Yes | We used fully-connected neural networks with two hidden layers. The input was the state u, and the output represented the first integrals V for FINDE, time-derivative ˆf for NODE, or the Hamiltonian H for HNN. Each hidden layer had 200 units and preceded a hyperbolic tangent activation function. Each weight matrix was initialized as an orthogonal matrix. ... The base model and FINDE were jointly trained using the Adam optimizer (Kingma & Ba, 2015) with the parameters (β1, β2) = (0.9, 0.999) and a batch size of 200. The learning rate was initialized to 10^-3 and decayed to zero with cosine annealing (Loshchilov & Hutter, 2017). |