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.
Position: Optimization in SciML Should Employ the Function Space Geometry
Authors: Johannes Müller, Marius Zeinhofer
ICML 2024 | Venue PDF | LLM Run Details | Input Tokens: 23,989 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 4,225 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | An illustration of the importance of the infinite-dimensional perspective is provided in Figure 1, which demonstrates that respecting the function space geometry can result in orders of magnitude improvement. Training curves for a PINN for a 2-dimensional Poisson equation; the first order optimizers (Adam and Gradient Descent) plateau, the second-order optimizers (ENGD and Newton) perform much better, but the function-space inspired optimizer (ENGD) reaches the highest accuracy by several orders of magnitude. |
| Researcher Affiliation | Collaboration | 1Chair of Mathematics of Information Processing, RWTH Aachen University, Aachen, Germany 2Simula Research Laboratory, Oslo, Norway. |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any concrete access to source code for the methodology described. |
| Open Datasets | No | The paper states that for PINNs, |
| Dataset Splits | No | The paper discusses training but does not provide specific dataset split information (e.g., percentages or counts for training, validation, or test sets). |
| Hardware Specification | No | The paper mentions |
| Software Dependencies | No | The paper does not provide specific ancillary software details with version numbers (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | No | The paper mentions different optimizers (Adam, Gradient Descent, ENGD, Newton) in the context of Figure 1 but does not provide specific hyperparameter values or detailed training configurations (e.g., learning rate, batch size, number of epochs) for the experiments. |