Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities
Authors: Takashi Matsubara, Takaharu Yaguchi
ICLR 2023 | Venue PDF | 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 EMAIL Takaharu Yaguchi Kobe University Kobe, Hyogo, 657 8501 Japan EMAIL |
| 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). |