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 [1].
Discovering Symmetries of ODEs by Symbolic Regression
Authors: Paul Kahlmeyer, Niklas Merk, Joachim Giesen
AAAI 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We provide examples on which our symbolic regression method finds symmetry generators while the established algebraic symmetry finding methods struggle to do so. That is, the symbolic regression approach enlarges the set of problems that can be tackled by symmetry finding methods. ... We demonstrate the added value of the symbolic regression approach on ten representative ODE systems for which Mathematica does not find an explicit solution directly, that is, without the SYM package. |
| Researcher Affiliation | Academia | Friedrich Schiller University Jena EMAIL, EMAIL, EMAIL |
| Pseudocode | No | The paper describes the method in prose and through a flowchart in Figure 4, but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide explicit statements about the release of source code for the methodology described, nor does it include any links to code repositories. |
| Open Datasets | No | The paper uses generated data from 'ten representative ODE systems' for evaluation, but it does not refer to or provide concrete access information (like links, DOIs, or repository names) for pre-existing public or open datasets. |
| Dataset Splits | No | The paper describes generating sample data from ODEs to evaluate a loss function, but it does not specify any training, test, or validation dataset splits in the conventional sense for machine learning experiments. |
| Hardware Specification | Yes | running Python 3.10 on an Intel Xeon Gold 6226R 64-core processor with 128 GB of RAM. |
| Software Dependencies | No | The paper mentions 'running Python 3.10' and uses 'Py Torch' and 'sympy' but does not provide specific version numbers for these libraries used in the experimental setup. |
| Experiment Setup | Yes | For our task of finding symmetries of ODE systems, we need to replace this loss function by a loss function that is based on the symmetry condition. Such a loss function is constructed as follows: Let f : Rd+1 Rd be the symbolic form of the ODE system under investigation. We first solve the ODE numerically by the Runge-Kutta algorithm (Dormand and Prince 1980) that computes a sample D = ti, y(ti) i=1,...,n of the ODE system s solution. ... The loss of the candidate symmetry generator η is then given as LD,f(η ) = 1/|D| P(t,y)∈D Pk=1 d Sk η (t, y) 2 . ... our implementation discards candidate expression DAGs for η where the median absolute value of η evaluated at the data points is smaller than a threshold value of ε = 0.01. |