Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Discovering Symbolic Partial Differential Equation by Abductive Learning
Authors: En-Hao Gao, Cunjing Ge, Yuan Jiang, Zhi-Hua Zhou
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results on three benchmarks across different noise levels demonstrate the effectiveness of our approach in PDE discovery. |
| Researcher Affiliation | Academia | En-Hao Gao, Cunjing Ge, Yuan Jiang, Zhi-Hua Zhou National Key Laboratory for Novel Software Technology, Nanjing University, China School of Artificial Intelligence, Nanjing University, China EMAIL, EMAIL |
| Pseudocode | Yes | Algorithm 1 presents the details of MSS. In the first stage (cf. Line 2-3), MSS evaluates expression terms in the library and calls Pareto Optimization for Subset Selection (POSS) [21, 30] to find a reduced term library sub Lib whose size should be no greater than the initial sparsity. |
| Open Source Code | Yes | Code is available at: https://github.com/AbductiveLearning/ABL-PDE. |
| Open Datasets | Yes | We use data from public datasets [2], incorporating 5% and 10% Gaussian noise to simulate inaccurate measurements as in [27]. |
| Dataset Splits | Yes | The training data consists of 1 × 10^4 (40%), 2 × 10^4 (40%), and 2 × 10^5 (20%) measurement points for the Burgers, Schrödinger, and Navier-Stokes experiments, respectively. We hold out 20% of the training data as a validation set, which is used to select the derivative computation weights and the hyperparameter λ. |
| Hardware Specification | Yes | All experiments were conducted on a server equipped with four NVIDIA A6000 GPUs, each with 48 GB of memory. |
| Software Dependencies | No | The paper does not provide specific version numbers for software dependencies. While it mentions the use of 'PINNs-Torch' in a reference, it does not specify its version or other software versions required for reproducibility in the main text or appendices. |
| Experiment Setup | Yes | Our model s architecture is a multilayer perceptron (MLP) composed of 8 hidden layers. For the Burgers Equation, each layer has 20 neurons. This architecture is adapted for the Schrödinger Equation by modifying the output layer to predict two variables (the real and imaginary parts of the solution). For the more complex Navier-Stokes Equations, we increase the network s width to 40 neurons per hidden layer. The networks are pre-trained for 5,000 epochs for the Burgers and Schrödinger equations, and 100,000 epochs for the Navier-Stokes equations. Across all tasks, we use a consistent initial sparsity of 10 and a margin threshold of 0.05. During consistency optimization, MSS is applied every 1,000 epochs to refine the discovered equation. The values for λ are selected based on validation error and are summarized in Table 4. |