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; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1]
Learning Green's functions associated with time-dependent partial differential equations
Authors: Nicolas Boullé, Seick Kim, Tianyi Shi, Alex Townsend
JMLR 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we attempt to provide theoretical foundations to understand the amount of training data needed to learn time-dependent PDEs. [...] While we exclusively focus on theory, the insights provided by this work will be of interest to a broader audience in scientific machine learning and motivate future empirical works and novel physics-informed neural network architectures. |
| Researcher Affiliation | Academia | Nicolas Boull e EMAIL Mathematical Institute University of Oxford Oxford, OX2 6GG, UK; Seick Kim EMAIL Department of Mathematics Yonsei University Seoul, 03722, ROK; Tianyi Shi EMAIL Center for Applied Mathematics Cornell University Ithaca, NY 14853, USA; Alex Townsend EMAIL Department of Mathematics Cornell University Ithaca, NY 14853, USA. All listed institutions are universities. |
| Pseudocode | No | The paper describes a "randomized algorithm" conceptually in Theorem 10 but does not provide any explicitly labeled pseudocode blocks or algorithms with structured steps. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code for the methodology described, nor does it provide a link to a code repository. The license mentioned is for the paper itself, not for its code. |
| Open Datasets | No | The paper discusses learning from "random input-output data" as part of its theoretical framework but does not refer to or provide access information for any specific publicly available dataset used for empirical evaluation. |
| Dataset Splits | No | The paper is theoretical and does not perform experiments on specific datasets; therefore, it does not provide dataset split information. |
| Hardware Specification | No | The paper is theoretical and does not describe any experiments requiring specific hardware for execution. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific software or library dependencies with version numbers for experimental reproduction. |
| Experiment Setup | No | The paper is theoretical, focusing on mathematical results and learning rates. It does not describe any experimental setup details such as hyperparameters or training configurations. |