Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space
Authors: Xihang Yue, Yi Yang, Linchao Zhu
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through extensive experiments across diverse PDE problems, we demonstrate that HPM consistently outperforms state-of-the-art methods in both accuracy and computational efficiency, while maintaining strong generalization capabilities with limited training data and excellent zero-shot performance on unseen resolutions. |
| Researcher Affiliation | Academia | 1The State Key Lab of Brain-Machine Intelligence, Zhejiang University, Hangzhou, China 2College of Computer Science and Technology, Zhejiang University, Hangzhou, China. Correspondence to: Linchao Zhu <EMAIL>. |
| Pseudocode | No | The paper describes mathematical formulations and network architectures but does not include any explicit pseudocode or algorithm blocks. |
| Open Source Code | Yes | 1Code: https://github.com/yuexihang/HPM |
| Open Datasets | Yes | The experimental problems include two regular domain problems Darcy Flow and Navier-Stokes from Li et al. (2020), and two irregular domain problems Airfoil and Plasticity from Li et al. (2023a). ... The evaluated problems include Irregular Darcy, Pipe Turbulence, Heat Transfer, Composite, and Blood Flow from Chen et al. (2023). |
| Dataset Splits | Yes | For Darcy Flow and Navier-Stokes, ... 1000 trajectories for training and an additional 200 data for testing. ... For Airfoil, 1000 samples are used for training and additional 200 samples are used for evaluation. ... For Irregular Darcy, ... trained on 1000 trajectories and tested on an extra 200 trajectories. ... For Pipe Turbulence, ... we utilize 300 trajectories for training and then test the models on 100 samples. |
| Hardware Specification | Yes | All experiments (including all baselines, ablations and our method) could be conducted with a single A100 device. ... We compare the inference time of different methods on the Airfoil problem, using a single RTX 3090 with batch size 1. |
| Software Dependencies | No | We used the toolkit of Paddle Paddle to develop this new model and solved the problem. ... we use the robust-laplacian library2 to compute these eigenfunctions (Sharp & Crane, 2020). This text mentions software but does not specify version numbers for Paddle Paddle or robust-laplacian library. |
| Experiment Setup | Yes | The implementation detail for each problem is presented in Table 8. ... Table 8. Implementation detail for each PDE problem. Problems Model Configurations Training Configurations Depth Width Head Number k Optimizer Scheduler Initial Lr Weight Decay Epochs Batch Size Darcy Flow 8 128 8 128 Adam W One Cycle LR 1e-3 1e-5 500 4 ... |