Lie Point Symmetry Data Augmentation for Neural PDE Solvers
Authors: Johannes Brandstetter, Max Welling, Daniel E Worrall
ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We ran experiments across different equations (Section 4.2), models (Section 4.3), training setups (Section 4.4), and choices of symmetries (Section 4.5). We tested the effectiveness of adding symmetries on raw generalization performance and survival time and demonstrate that adding LPSDA is equivalent to using larger training sets by up to a factor of 16 in size on the datasets used. We also probe the effect of LPSDA on long rollout stability (Section 4.6), and we measure the equivariance error of the learned models, comparing with classical solvers (Section 4.7). |
| Researcher Affiliation | Collaboration | 1University of Amsterdam 2Johannes Kepler University Linz now at Microsoft Research 3Qualcomm AI Research, an initiative of Qualcomm Technologies, Inc now at Deepmind. |
| Pseudocode | No | The paper describes the data augmentation process schematically in Figure 2 and training methodologies in Figure 3, but it does not contain explicit pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | Yes | Code available at https://github.com/brandstetter-johannes/LPSDA. |
| Open Datasets | No | The paper states that numerical groundtruth data for the Kd V, KS, and Burgers equations was “obtained” or “solved” (e.g., “Numerical groundtruth data for the Korteweg-de Vries... is obtained on a periodic domain...”), indicating custom generation rather than the use of a pre-existing, publicly available dataset with specific access details. |
| Dataset Splits | No | The paper mentions “training set” and “test NMSE” (e.g., “We compare test set normalized MSE... across training set sizes”) but does not explicitly provide details about a validation dataset split (e.g., percentages, sample counts, or specific named splits). |
| Hardware Specification | Yes | training for the different experiments takes between 12 and 24 hours on average on a Ge Force RTX 2080 Ti GPU. |
| Software Dependencies | No | The paper mentions software components such as “Adam W optimizer,” “1D Res Net-like model,” “Fourier Neural Operator (FNO),” and “scipy.fftpack,” but it does not specify concrete version numbers for these software dependencies. |
| Experiment Setup | Yes | We optimize models using the Adam W optimizer (Loshchilov & Hutter, 2017) with learning rate 1e-4, weight decay 1e-8 for 20 epochs and minimize the normalized mean squared error (NMSE) which is outlined in Equation 20. |