Physics-Informed Diffusion Models
Authors: Jan-Hendrik Bastek, WaiChing Sun, Dennis Kochmann
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. |
| Researcher Affiliation | Academia | Jan-Hendrik Bastek Dept. of Mechanical and Process Eng. ETH Zurich Zurich, Switzerland EMAIL; Wai Ching Sun Dept. of Civil Eng. and Eng. Mechanics Columbia University New York, NY, USA EMAIL; Dennis M. Kochmann Dept. of Mechanical and Process Eng. ETH Zurich Zurich, Switzerland EMAIL |
| Pseudocode | Yes | Algorithm 1 Physics-informed diffusion model training |
| Open Source Code | Yes | Code is available at https://github.com/jhbastek/Physics Informed Diffusion Models. |
| Open Datasets | Yes | We again consider a square domain Ω= [0, 1]2 and benchmark our proposed PIDM to state-of-the-art frameworks (Mazé & Ahmed, 2023; Giannone et al., 2023) that also provide a dataset consisting of 30,000 optimized structures with various boundary conditions and volume constraints and two proposed test scenarios with inand out-of-distribution boundary conditions. |
| Dataset Splits | Yes | We create a training and a validation dataset of 10,000 and 1,000 datapoints, respectively, by solving the governing equations (see equation 29) for a sampled permeability field on a 64 64 grid. |
| Hardware Specification | Yes | All models were trained on a single Nvidia Quadro RTX Quadro RTX 6000 GPU equipped with 24GB GDDR6 memory. |
| Software Dependencies | No | The model is implemented and trained using Py Torch (Paszke et al., 2019). Finite difference stencils are implemented via torch.nn.Conv2D (Paszke et al., 2019) with a custom kernel, which we can precompute for stencils up to arbitrary order via findiff (Baer, 2018). We solve for the over-determined pressure field using the scipy.linalg.lstsq (Virtanen et al., 2020) solver with default settings. |
| Experiment Setup | Yes | We train the model for 400 epochs on 10,000 randomly sampled points of the unit circle, using the Adam optimizer (Kingma & Ba, 2014) with a learning rate of 5 10 4. We use a batch size of 128, and 100 diffusion timesteps with a cosine scheduler (Dhariwal & Nichol, 2021). |