GridMix: Exploring Spatial Modulation for Neural Fields in PDE Modeling
Authors: Honghui Wang, Shiji Song, Gao Huang
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The effectiveness of MARBLE is extensively validated on diverse benchmarks encompassing dynamics modeling and geometric prediction. ... We assessed the flexibility of our model by applying it to two different tasks: forecasting the temporal dynamics of a physical system (see Section 4.1) and predicting the steady-state behavior based on domain geometry (see Section 4.2). ... Results. Table 2 comprehensively evaluate the temporal extrapolation capabilities of various machine learning models... |
| Researcher Affiliation | Academia | Honghui Wang, Shiji Song & Gao Huang Department of Automation, BNRist, Tsinghua University, Beijing, China, EMAIL, EMAIL |
| Pseudocode | No | The paper does not contain any sections explicitly labeled "Pseudocode" or "Algorithm", nor does it present structured steps in a code-like format. |
| Open Source Code | Yes | The code will be available on https://github.com/Leap Lab THU/Grid Mix. ... Additionally, our code is included in the supplementary materials. |
| Open Datasets | Yes | A.1 DYNAMICS MODELING: 2D-Navier-Stokes (Navier-Stokes). We examine the 2D Navier-Stokes equation as detailed in Li et al. (2021); Yin et al. (2022); Serrano et al. (2023)... 3D-Spherical Shallow-Water (Shallow-Water)... Data generation was carried out using the Dedalus framework (Burns et al., 2020), following the configuration described in Yin et al. (2022)... A.2 GEOMETRIC-AWARE INFERENCE: We utilize datasets from Li et al. (2023b)... |
| Dataset Splits | Yes | Each resulting trajectory contains 40 snapshots. We split these trajectories into two segments: the first 20 frames are utilized for training (denoted as In-t), while the remaining 20 frames are reserved for testing... In total, we generated 256 trajectories for training and 16 for evaluation. ... These long trajectories were then segmented into sub-trajectories of 40 timestamps each, resulting in 64 training trajectories and 8 testing trajectories. ... The dataset consists of 1000 training examples and 200 test examples... |
| Hardware Specification | Yes | All experiments were conducted on an NVIDIA A100 GPU. |
| Software Dependencies | No | The paper mentions software tools like the "Dedalus framework" for data generation and refers to the "CORAL paper (Serrano et al., 2023)" for experimental setup, but it does not specify version numbers for any ancillary software dependencies used in their own method's implementation (e.g., Python, PyTorch, CUDA versions). |
| Experiment Setup | Yes | To train our model, we follow the experimental setup and hyperparameter choices as outlined in the original CORAL (Serrano et al., 2023) paper. The additional hyperparameters for MARBLE are listed in Table 6. (Table 6 lists specific hyperparameters like grid resolution, basis functions count, latent dimension, basis learning rate, and SDA sampling ratio for different datasets.) |