Symmetry-Informed Governing Equation Discovery
Authors: Jianke Yang, Wang Rao, Nima Dehmamy, Robin Walters, Rose Yu
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In experiments across diverse dynamical systems, our approach demonstrates better robustness against noise and recovers governing equations with significantly higher probability than baselines without symmetry. |
| Researcher Affiliation | Collaboration | Jianke Yang UCSD Wang Rao Tsinghua University Nima Dehmamy IBM Research Robin Walters Northeastern University Rose Yu UCSD |
| Pseudocode | No | The paper does not contain pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | Yes | Our codebase is available at https://github.com/Rose-STL-Lab/symmetry-ode-discovery. |
| Open Datasets | No | The paper describes how the data was generated ('For each ODE system, we sample N random initial conditions x0 from a uniform distribution on a specified subset of X Rd. Starting from each initial condition, we integrate the ODE using the 4th-order Runge-Kutta (RK4) method and sample with a regular step size t to get the discrete trajectory x0:T.') but does not provide a direct link, DOI, or repository for the generated datasets themselves, nor does it refer to them as publicly available. |
| Dataset Splits | Yes | We generate 50 trajectories for training, 10 for validation, and 10 for training, with T = 100 timesteps sampled at a fixed rate t = 0.2. (Damped Oscillator) We generate 100 trajectories for training, 20 for validation, and 20 for testing, with T = 100 timesteps sampled at a fixed rate t = 0.02. (Growth) We generate 200 trajectories for training, 20 for validation, and 20 for testing, with T = 10000 timesteps sampled at a fixed rate t = 0.002. (Lotka-Volterra) We generate 10 trajectories for training, 2 for validation, and 2 for testing, with T = 10000 timesteps sampled at a fixed rate t = 0.002. (Glycolytic Oscillator) |
| Hardware Specification | No | The paper mentions in the checklist justification that 'most experiments are solving low-dimensional problems and can be done within minutes on a single CPU or GPU,' but it does not specify any particular CPU or GPU models or other specific hardware details in the main paper or its appendices. |
| Software Dependencies | No | The paper mentions using 'Py SR package (Cranmer, 2023)' and 'sympy (Meurer et al., 2017)' but does not provide specific version numbers for these or other software dependencies. |
| Experiment Setup | Yes | For all algorithms based on sparse regression (SINDy), we use a function library Θ(x) that contains up to second-order polynomials, with an exception for Lotka-Volterra system where we also include the exponential terms. We apply sequential thresholding (Brunton et al., 2016) to enforce parsimony in the equations. The threshold is set to 0.05 for the damped oscillator and the growth system, 0.075 for the glycolytic oscillator, and 0.15 for the Lotka-Volterra system. The same threshold is applied to all methods including SINDy, WSINDy and Equiv SINDy. ... For our equivariant models based on symmetry regularization, we use the L-BFGS algorithm (Nocedal, 1980) for optimizing the SINDy parameters. |