Message Passing Neural PDE Solvers
Authors: Johannes Brandstetter, Daniel E. Worrall, Max Welling
ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, discretization, etc. in 1D and 2D. |
| Researcher Affiliation | Collaboration | Johannes Brandstetter University of Amsterdam Johannes Kepler University Linz brandstetter@ml.jku.at Daniel E. Worrall Qualcomm AI Research dworrall@qti.qualcomm.com Max Welling University of Amsterdam m.welling@uva.nl |
| Pseudocode | Yes | Pseudocode for one training step using the pushforward trick and temporal bundling is sketch in Algorithm 1. |
| Open Source Code | Yes | For reproducibility, we provide our at https://github.com/brandstetter-johannes/MP-Neural-PDESolvers. |
| Open Datasets | No | All data used in this work is generated by ourselves. It is thus of great importance to make sure that the produced datasets are correct. We therefore spend an extensive amount of time cross-checking our produced datasets. |
| Dataset Splits | Yes | Our training sets consist of 2096 trajectories, downsampled to resolutions (nt, nx) {(250, 100), (250, 50), (250, 40)}. Numerical groundtruth is generated using a 5th-order WENO scheme (WENO5) (Shu, 2003) for the convection term xu2 and 4th-order finite difference stencils for the remaining terms. The temporal solver is an explicit Runge-Kutta 4 solver (Runge, 1895; Kutta, 1901) with adaptive timestepping. |
| Hardware Specification | Yes | Runtimes are for one full unrolling over 250 timesteps on a Ge Force RTX 2080 Ti GPU. ...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 using AdamW optimizer (Loshchilov & Hutter, 2017) and Swish (Ramachandran et al., 2017) activation functions, but does not provide specific version numbers for software dependencies or libraries like Python, PyTorch, or TensorFlow. |
| 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 root mean squared error (RMSE). We use batch size 16 for experiments E1-E3 and WE1-WE3 and batch size of 4 for 2D experiments. ...We use Swish (Ramachandran et al., 2017) activation functions for experiments E1-E3 and WE1WE3 and Re LU activation for the 2D experiments. |