Explicit Discovery of Nonlinear Symmetries from Dynamic Data
Authors: Lexiang Hu, Yikang Li, Zhouchen Lin
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | On top quark tagging and a series of dynamic systems, Lie NLSD shows qualitative advantages over existing methods and improves the long rollout accuracy of neural PDE solvers by over 20% while applying to guide data augmentation. In this section, we evaluate Lie NLSD on top quark tagging (Section 5.2) and a series of dynamic systems (Section 5.3). |
| Researcher Affiliation | Academia | 1State Key Lab of General AI, School of Intelligence Science and Technology, Peking University 2Institute for Artificial Intelligence, Peking University 3Pazhou Laboratory (Huangpu), Guangzhou, Guangdong, China. Correspondence to: Zhouchen Lin <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Lie NLSD |
| Open Source Code | Yes | Code and data are available at https://github.com/hulx2002/Lie NLSD. |
| Open Datasets | Yes | We first evaluate the ability of Lie NLSD to discover linear symmetries on top quark tagging (Kasieczka et al., 2019). |
| Dataset Splits | Yes | We sample M = 100 points from the training set to construct C R100 16 in Equation (13) (in practice, we construct C C R16 16). |
| Hardware Specification | No | No specific hardware details (GPU models, CPU types, or cloud computing platforms with specifications) are provided in the paper. |
| Software Dependencies | No | No specific version numbers for key software components or libraries are provided. The paper mentions the 'Adan optimizer' but without a version or broader software stack details. |
| Experiment Setup | Yes | We use an MLP with 3 hidden layers and hidden dimension 200 to fit the mapping. The sample size for symmetry discovery is M = 100. For Lie GAN, we set the dimension of the Lie algebra basis to 7, using an MLP with 2 hidden layers and hidden dimension 512 as the discriminator... For training, we set the batch size to 256 and use the Adan optimizer (Xie et al., 2024) with a learning rate of 10-3. For symmetry discovery, we consider the singular values smaller than ϵ2 = 10-2 as the effective information of the symmetry group... For basis sparsification, we set ϵ1 = 10-2 and ϵ2 = 10-1... |