Physics and Lie symmetry informed Gaussian processes

Authors: David Dalton, Dirk Husmeier, Hao Gao

ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Experimental results demonstrate that the use of symmetry constraints improves the performance of the GP for both forward and inverse problems, and that our approach offers competitive performance with neural networks in the low-data environment.
Researcher Affiliation Academia 1School of Mathematics and Statistics, University of Glasgow, United Kingdom. Correspondence to: David Dalton <david.dalton@glasgow.ac.uk>.
Pseudocode No No pseudocode or clearly labeled algorithm blocks were found in the paper.
Open Source Code Yes Code and data are available at github.com/dodaltuin/jaxpigp/tree/main/examples/PSGPs.
Open Datasets No The paper describes generating datasets based on PDEs and resampling, but does not provide concrete access information (link, DOI, formal citation) to a publicly available or open dataset that was used for training.
Dataset Splits No The paper does not explicitly provide details about a validation dataset split (e.g., percentages, sample counts, or predefined splits). It mentions 'test set results' but no specific validation split.
Hardware Specification No No specific hardware details (e.g., GPU/CPU models, memory amounts, or cloud instance types) used for running experiments were mentioned in the paper.
Software Dependencies No The paper mentions 'Python using JAX' but does not specify version numbers for Python, JAX, or any other software libraries or dependencies. 'Adam optimiser' is mentioned, but it's an algorithm, not a versioned software component.
Experiment Setup Yes For the GP models, kuu was specified to be the rational quadratic kernel. We experimented with different neural network architectures (using tanh activation function), and found that four hidden layers each of width 20 yielded the best accuracy. Each model was trained using the Adam optimiser with exponentially decaying learning rate (Kingma & Ba, 2017). As suggested in (Long et al., 2022), we use the whitening trick (Murray & Adams, 2010) when evaluating the ELBO (Eq. (21)), to improve training efficiency. Noise levels were set to 1% in each case see Appendix B for results under different levels of noise.