MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation
Authors: Qi Wang, Yuan Mi, Wang Haoyun, Yi Zhang, Ruizhi Chengze, Hongsheng Liu, Ji-Rong Wen, Hao Sun
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments across various PDE systems, including the Navier-Stokes equations, demonstrate that Multi PDENet can accurately predict long-term spatiotemporal dynamics, even given small and incomplete training data, e.g., spatiotemporally down-sampled datasets. Multi PDENet achieves the state-of-the-art performance compared with other neural baseline models, also with clear speedup compared to classical numerical methods. |
| Researcher Affiliation | Collaboration | 1Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China 2Huawei Technologies, Shenzhen, China. Correspondence to: Hao Sun <EMAIL>. |
| Pseudocode | No | The paper describes the methodology in detail within Section 3 and uses figures like Figure 1, but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our source codes are available in the following Git Hub repository: https://github.com/intell-sci-comput/Multi PDENet. |
| Open Datasets | No | We generate the data using high-order FD/FV methods with high resolution under periodic boundary conditions and then downsample it spatially and temporally to a coarse grid. The low-resolution dataset is used for both training and testing. We consider four distinct dynamical systems: Korteweg-de Vries (Kd V), Burgers, Gray-Scott (GS), and Navier-Stokes equations (NSE). |
| Dataset Splits | Yes | Each dataset is divided into 90% for training and 10% for validation. We segment trajectories into data series, where each sample includes multi snapshots (e.g., for the Kd V dataset, the sample length is set to 10, as detailed in Table 1) separated by a time step t, the 2nd to the last snapshot serves as the training labels. During training, we use only 3 5 trajectories for each system, and evaluate them on 10 distinct trajectories. |
| Hardware Specification | Yes | All experiments (both training and inference) in this study were conducted on a single Nvidia A100 GPU (with 80GB memory) running on a server with an Intel(R) Xeon(R) Platinum 8380 CPU (2.30GHz, 64 cores). |
| Software Dependencies | No | Nevertheless, we also would like to clarify that the DNS code used above was implemented in JAX, while our model was programmed in Py Torch. |
| Experiment Setup | Yes | The Multi PDENet architecture employs the Adam optimizer with a learning rate of 5 10 3. The model is trained over 1000 epochs with a batch size of 90. Detailed settings for the rollout timestep can be found in Table 1. Additionally, we use the Step LR scheduler to adjust the learning rate by a factor of 0.96 every 200 steps. The model hyperparameters are listed in Tables S5 and S6. |