Active Learning with Selective Time-Step Acquisition for PDEs
Authors: Yegon Kim, Hyunsu Kim, Gyeonghoon Ko, Juho Lee
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the effectiveness of our method on several benchmark PDEs, including the Burgers equation, Korteweg De Vries equation, Kuramoto Sivashinsky equation, the incompressible Navier-Stokes equation, and the compressible Navier-Stokes equation. Experiments show that our approach improves performance by large margins over the best existing method. |
| Researcher Affiliation | Academia | 1 Korea Advanced Institute of Science and Technology, Daejeon, Korea. Correspondence to: Yegon Kim <EMAIL>, Juho Lee <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 provides an overview of our framework. Fig. 2 also provides an illustrated version of the overview. |
| Open Source Code | Yes | Our code is publicly available at https://github.com/yegonkim/stap. |
| Open Datasets | No | The paper describes generating data from numerical solvers for various PDEs based on sampled initial conditions, rather than using a pre-existing publicly available dataset. There are no specific links, DOIs, or formal citations to a downloadable dataset. |
| Dataset Splits | Yes | The pool set has 10,000 initial conditions, and we always start with an initial dataset of 32 fully sampled trajectories. The initial conditions in the test set are sampled from the same distribution as those in the pool set. An ensemble size of M = 2 is used... The test set always consists of 1,000 trajectories, on which several error metrics are defined. |
| Hardware Specification | Yes | All experiments were conducted on 8 NVIDIA GeForce RTX 2080 Ti GPUs, and the results are averages from 5 seed values. The wall-clock time of each baseline method and STAP is measured with a single NVIDIA GeForce RTX 2080 Ti GPU, and summarized in Table 3. |
| Software Dependencies | No | The paper mentions optimizers (Adam) and schedulers (cosine annealing) by name and citation, but does not provide specific version numbers for these or any other software libraries (e.g., PyTorch, TensorFlow, NumPy, SciPy) that would be needed for replication. |
| Experiment Setup | Yes | All models have four hidden layers with 64 channels in each layer. We use 32, 256, 128, 16, and 32 Fourier modes for Burgers, Kd V, KS, INS and CNS equations, respectively. All models were trained with Adam (Kingma, 2014) for 100 epochs, using a learning rate of 10 3, a batch size of 32, and a cosine annealing scheduler (Loshchilov and Hutter, 2016). An ensemble size of M = 2 is used... We perform 10 rounds of acquisition, and the budget of each round is set to B = 8 L where L is the length of a full trajectory. |