Notice: This website is continuously updated as new conference proceedings and journal volumes are published. Consequently, the figures presented here may differ from those reported in our publications.
A brief overview of our methodology is provided on the Methods page, along with references to publications documenting our approach and links to the code and data used in each study.
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.
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective
Authors: Tanya Marwah, Zachary Chase Lipton, Jianfeng Lu, Andrej Risteski
ICML 2023 | Venue PDF | LLM Run Details | Input Tokens: 34,214 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 4,429 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | However, most prior theoretical analyses have been limited to linear PDEs. In this work, we take a step towards studying the representational power of neural networks for approximating solutions to nonlinear PDEs. Our proof technique involves neurally simulating (preconditioned) gradient in an appropriate Hilbert space |
| Researcher Affiliation | Academia | 1Carnegie Mellon University 2Duke University. |
| Pseudocode | No | The paper describes mathematical algorithms and iterative processes but does not include a clearly labeled pseudocode or algorithm block. |
| Open Source Code | No | The paper is theoretical and does not mention the release of source code for the described methodology. |
| Open Datasets | No | The paper is theoretical and does not describe experiments using datasets. |
| Dataset Splits | No | The paper is theoretical and does not describe experiments or dataset splits for training or validation. |
| Hardware Specification | No | The paper is theoretical and does not mention any hardware specifications for running experiments. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup or hyperparameters. |