Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution
Authors: Rui Wang, Elyssa Hofgard, Han Gao, Robin Walters, Tess Smidt
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We provide both theoretical and empirical evidence that this flexible convolution technique allows the model to maintain the highest level of equivariance that is consistent with data and discover the subtle symmetry-breaking factors in various physical systems. We employ various relaxed group convolution architectures to uncover various symmetry-breaking factors that are interpretable and physically meaningful in different physical systems, including the phase transition of crystal structure, the isotropy and homogeneity breaking in turbulent flow, and the time-reversal symmetry breaking in pendulum systems. |
| Researcher Affiliation | Academia | 1Massachusetts Institute of Technology 2Harvard University 3Northeastern University. Correspondence to: Rui Wang <rayruw@mit.edu>. |
| Pseudocode | No | The paper does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | We open-source our code at https: //github.com/atomicarchitects/ Symmetry-Breaking-Discovery. |
| Open Datasets | Yes | We use the Cartesian coordinates of Ba Ti O3 in cubic, tetragonal, and orthorhombic phases from the Material Project (Jain et al., 2013). We use a 2D direct numerical simulation of a turbulent boundary layer flow/channel flow from Gao et al. (2023) |
| Dataset Splits | Yes | We employ an 80%-20% split for training and validation and use early stopping based on the validation loss. We split the data 80%-10%-10% for training-validation-test across time and report mean absolute errors over three random runs. |
| Hardware Specification | No | This research used resources of the National Energy Research Scientific Computing Center (NERSC) under Award Number ERCAP0028753, a Department of Energy Office of Science User Facility. |
| Software Dependencies | No | The paper mentions "Phi Flow (Holl et al. (2020))" but does not specify its version number or any other software dependencies with version details. |
| Experiment Setup | Yes | The models are trained to generate 643 simulations from 163 downsampled versions of themselves. We use the L1 loss function over the L2 loss, as it significantly enhances performance. We split the data 80%-10%-10% for training-validation-test across time and report mean absolute errors over three random runs. As for hyperparameter tuning, except for fixing the number of layers and kernel sizes, we perform a grid search for the learning rate, hidden dimensions, batch size, and the number of filter bases for all three types of models. |