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..
Operator Learning for Hyperbolic PDEs
Authors: Christopher Wang, Alex Townsend
JMLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We also include numerical experiments which corroborate our theoretical findings. Keywords: Data-driven PDE learning, hyperbolic PDE, operator learning, low-rank approximation, randomized SVD. A numerical implementation and example of our algorithm is presented in Section 5. Finally, we summarize our results and discuss further directions of research in Section 6. Figure 6: Empirical rate of convergence of Algorithm 2. |
| Researcher Affiliation | Academia | Christopher Wang EMAIL Department of Mathematics Cornell University Ithaca, NY 14853, USA. Alex Townsend EMAIL Department of Mathematics Cornell University Ithaca, NY 14853, USA. |
| Pseudocode | Yes | Algorithm 1 Approximating F via r SVD. Algorithm 2 Learning the solution operator via input-output data. Algorithm 3 Detecting the numerical rank of F in a subdomain. |
| Open Source Code | Yes | MATLAB code is available at https://github.com/chriswang030/OperatorLearningforHPDEs. |
| Open Datasets | No | Input-output data was generated using the known analytical expression for the true Green s function. The paper does not provide concrete access information for a publicly available or open dataset. |
| Dataset Splits | No | The paper discusses |
| Hardware Specification | No | The paper does not provide specific hardware details for running the experiments. It generally refers to |
| Software Dependencies | No | We implement Algorithms 1, 2, and 3 in MATLAB for the constant coefficient wave operator Lu = utt 4uxx with homogeneous initial and boundary conditions. No specific version numbers are provided for MATLAB or any other software dependencies. |
| Experiment Setup | No | The paper mentions discretizing the domain |