Operator Learning for Hyperbolic PDEs
Authors: Christopher Wang, Alex Townsend
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | 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 |