Accelerating PDE-Constrained Optimization by the Derivative of Neural Operators
Authors: Ze Cheng, Zhuoyu Li, Wang Xiaoqiang, Jianing Huang, Zhizhou Zhang, Zhongkai Hao, Hang Su
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our extensive experimental results demonstrate the effectiveness of our model in accurately learning operators and their derivatives. Furthermore, our hybrid optimization approach exhibits robust convergence. |
| Researcher Affiliation | Collaboration | 1Bosch (China) Invest Ltd., Shanghai, China 2Dept. of Comp. Sci. & Techn., Institute for AI, BNRist Center, Tsinghua-Bosch Joint ML Center, Tsinghua University. Correspondence to: Ze Cheng <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Optimization with RNO Algorithm 2 Optimization-oriented training of RNO |
| Open Source Code | Yes | Our code is available at https://github.com/zechengai/OptRNO. |
| Open Datasets | No | No specific access information (link, DOI, citation to a public repository) is provided for the datasets. The paper mentions creating "four challenging optimization datasets from various physics backgrounds, all simulated using COMSOL 6.0." without indicating public availability. |
| Dataset Splits | Yes | Train and test sets are split in 8:2 by trajectories. |
| Hardware Specification | Yes | Experiments were conducted on both a laptop with CPU 2.5 GHz (11th Gen Intel i7) and a GPU Nvidia V100. |
| Software Dependencies | No | The paper mentions using "COMSOL 6.0" for data simulation and "Method of Moving Asymptotes (MMA) (Svanberg, 1987)" for optimization. However, it does not provide specific version numbers for other key software components, libraries, or frameworks used in their implementation. |
| Experiment Setup | Yes | We employed the Method of Moving Asymptotes (MMA) (Svanberg, 1987) and Gaussian smoothing for sensitivity updates. Input: RNO Gθ, random initial input λ0, learning rate η > 0, buffer list B with size N2, Ground truth solution ugt = None with empty initialization, warm up steps for optimization before the first validation, radius r around ugt as a criterion to trigger validation. Figure 5 presents the results, where the relative l2 error represents the average error across all components. R-VF outperforms both baselines and demonstrates strong performance on all α s. The reference dropout ratio is set at 0.3 to balance training performance. Let εi N(0, σ), where σ is set to 1% of the standard deviation of the input In our implementation, d = 2 and dr = 0.5. |