On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Authors: Ziang Chen, Jianfeng Lu, Yulong Lu
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper derives complexity estimates of the solutions of d-dimensional second-order elliptic PDEs in the Barron space... We prove under some appropriate assumptions that if the coefficients and the source term of the elliptic PDE lie in Barron spaces, then the solution of the PDE is ϵ-close with respect to the H1 norm to a Barron function. Moreover, we prove dimensionexplicit bounds for the Barron norm of this approximate solution... |
| Researcher Affiliation | Academia | Ziang Chen Department of Mathematics Duke University... Jianfeng Lu Departments of Mathematics, Physics, and Chemistry Duke University... Yulong Lu Department of Mathematics and Statistics Lederle Graduate Research Tower University of Massachusetts... |
| Pseudocode | No | The paper focuses on theoretical derivations and proofs, and does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper is theoretical and focuses on mathematical proofs and derivations; it does not mention releasing any source code for its methodology. |
| Open Datasets | No | This is a theoretical paper that does not involve empirical experiments or the use of datasets for training. |
| Dataset Splits | No | This is a theoretical paper that does not involve empirical experiments or data splitting for validation. |
| Hardware Specification | No | The paper is theoretical and does not describe any computational experiments that would require specific hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not describe any computational implementation details or software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup details, hyperparameters, or training configurations. |