HEAP: Hyper Extended A-PDHG Operator for Constrained High-dim PDEs
Authors: Mingquan Feng, Weixin Liao, Yixin Huang, Yifan Fu, Qifu Zheng, Junchi Yan
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirical results on a variety of high-dim PDEs show that HEAP outperforms the state-of-the-art neural operator model. All experiments were conducted on a machine with 1TB memory, 144 cores Intel Xeon Platinum 8352V CPU, and 8 GPUs (NV Ge Force RTX 4090). We benchmark HEAP on four prototype equations, each tested in both an unconstrained form (suffix -UC) and a constrained form (suffix -C). Tables 2, 3, 4, 5, and 6 present experimental results including PDE residual, physical constraint violation, time and space usage, and ablation studies. |
| Researcher Affiliation | Academia | 1Sch. of Computer Science & Sch. of Artificial Intelligence, Shanghai Jiao Tong University, China. |
| Pseudocode | Yes | Algorithm 1 A-PDHG embodiment for solving QP in Eq. 3. Algorithm 2 Hyper-Extended A-PDHG (i.e. HEAP). |
| Open Source Code | Yes | Code available at GitHub. |
| Open Datasets | No | The paper defines the PDEs and initial conditions for generating data, e.g., "The training set consists of 150K randomly generated θ from normal distribution, and the test set is 250 randomly generated θ from another normal distribution with slightly different mean and variance." This describes how to generate the data rather than providing concrete access information to a pre-existing publicly available dataset. |
| Dataset Splits | Yes | The training set consists of 150K randomly generated θ from normal distribution, and the test set is 250 randomly generated θ from another normal distribution with slightly different mean and variance. Unless otherwise noted, the initial ansatz parameters θ0 are drawn i.i.d. from a Gaussian distribution with mean 0 and standard deviation 0.5 for training, and from a wider N(0, 1) for test; this encourages robustness to distribution shift while keeping the training residual numerically stable. |
| Hardware Specification | Yes | All experiments were conducted on a machine with 1TB memory, 144 cores Intel Xeon Platinum 8352V CPU, and 8 GPUs (NV Ge Force RTX 4090). |
| Software Dependencies | No | The paper mentions "Adam optimizer" and "Runge-Kutta" for integration, but does not provide specific version numbers for any software libraries or dependencies used. |
| Experiment Setup | Yes | The extended dimension of HEAP is 20; the iteration is 3, and the hypernetwork Nw is a 5-layer Res Net with 1000 hidden units. The HEAP is trained with Adam optimizer, default batch size 64, and 100 epochs. E.g., Table 1 summarises the settings used for CSO on our Burgers type equation experiments; HEAP employs the same configuration. The ODE is integrated with the Runge-Kutta (Butcher, 1996) with a time step 1/10 of the time horizon. To balance their magnitudes during optimisation we set λpde = 10 2, λpc = 1, and λnc = 10, respectively, for all experiments. |