On conditional diffusion models for PDE simulations
Authors: Aliaksandra Shysheya, Cristiana Diaconu, Federico Bergamin, Paris Perdikaris, José Miguel Hernández-Lobato, Richard Turner, Emile Mathieu
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this work, we perform a comparative study of score-based diffusion models for forecasting and assimilation of sparse observations. We empirically show that these modifications are crucial for successfully tackling the combination of forecasting and data assimilation, a task commonly encountered in real-world scenarios. |
| Researcher Affiliation | Collaboration | Aliaksandra Shysheya University of Cambridge as2975@cam.ac.uk Cristiana Diaconu University of Cambridge cdd43@cam.ac.uk Federico Bergamin Technical University of Denmark fedbe@dtu.dk Paris Perdikaris Microsoft Research AI4Science paperdikaris@microsoft.com José Miguel Hernández-Lobato University of Cambridge jmh233@cam.ac.uk Richard E. Turner University of Cambridge Microsoft Research AI4Science The Alan Turing Institute ret23@cam.ac.uk Emile Mathieu University of Cambridge ebm32@cam.ac.uk |
| Pseudocode | Yes | We provide in App. K pseudocode for each rollout strategy. (App. K contains Algorithm 1, Algorithm 2, Algorithm 3, Algorithm 4) |
| Open Source Code | Yes | The code to reproduce the experiments is publicly available at https://github.com/cambridge-mlg/pdediff. |
| Open Datasets | No | In this work, we consider the 1D Kuramoto-Sivashinsky (KS) and the 2D Kolmogorov flow equations... We generate the ground truth trajectories for the 1D Kuramoto-Sivashinsky equation... We use the setup described by [60] and their public repository to generate ground truth trajectories for the Kolmogorov-flow equation... Due to memory constraints, we are not able to share the exact data used for KS and Kolmogorov. However, we are providing all necessary instructions for data generation. |
| Dataset Splits | Yes | Training trajectories are of length 140 τ, while the length of validation and testing ones is set to 640 τ. The training set we used contains 819 trajectories, the validation set contains 102 trajectories, and we test all the different models on 50 test trajectories. |
| Hardware Specification | Yes | All models and the experiments we present in this paper were run on a single GPU. We used a GPU cluster with a mix of RTX 2080 Ti, RTX A5000, and Titan X GPUs. The majority of the GPUs we used have 11GB of memory. |
| Software Dependencies | No | Our implementation is built on Py Torch [50]. However, specific version numbers for PyTorch or other software dependencies are not provided, preventing full reproducibility based solely on the text. |
| Experiment Setup | Yes | For sampling, we use the DPM solver [44] with 128 evenly spaced discretisation steps. As a final step, we return the posterior mean over the noise free data via Tweedie s formula. For the guidance schedule we set r2 t = γσ2 t /µ2 t and tune γ via grid search. We refer to App. D.4 for more details. (App. D.4 provides specific hyperparameters for U-Net architecture, optimizer, learning rate, epochs, and batch size). |