Sharp Spectral Rates for Koopman Operator Learning
Authors: Vladimir Kostic, Karim Lounici, Pietro Novelli, Massimiliano Pontil
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments illustrate the implications of the bounds in practice. We illustrate various aspects of our theory with simple experiments. They have been implemented in Python using the library Kooplearn (available at https://github.com/CSML-IIT-UCL/ kooplearn) to fit the PCR and RRR estimators. Full details are in Appendix F. |
| Researcher Affiliation | Academia | Vladimir R. Kostic Istituto Italiano di Tecnologia University of Novi Sad vladimir.kostic@iit.it Karim Lounici CMAP-Ecole Polytechnique karim.lounici@polytechnique.edu Pietro Novelli Istituto Italiano di Tecnologia pietro.novelli@iit.it Massimiliano Pontil Istituto Italiano di Tecnologia University College London massimiliano.pontil@iit.it |
| Pseudocode | No | The paper describes algorithms using mathematical formulas and text but does not include any pseudocode or algorithm blocks. |
| Open Source Code | Yes | We illustrate various aspects of our theory with simple experiments. They have been implemented in Python using the library Kooplearn (available at https://github.com/CSML-IIT-UCL/ kooplearn) to fit the PCR and RRR estimators. Full details are in Appendix F. |
| Open Datasets | Yes | We use a realistic simulation of the small molecule Alanine Dipeptide already discussed in [24, 44]. |
| Dataset Splits | No | We use a realistic simulation of the small molecule Alanine Dipeptide already discussed in [24, 44]. We trained 19 RRR estimators each corresponding to a different kernel and then we evaluated the forecasting RMSE on 2000 initial conditions drawn from a test dataset. In Figure 3 we report these errors, highlighting the model with the smallest average empirical spectral bias (18) evaluated on 5000 validation points. The paper mentions "validation dataset" and "test dataset" but does not provide specific split percentages or counts for training data, nor a clear description of how these splits were created or if they are standard. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as GPU/CPU models or memory used for the experiments. |
| Software Dependencies | No | They have been implemented in Python using the library Kooplearn (available at https://github.com/CSML-IIT-UCL/ kooplearn) to fit the PCR and RRR estimators. The paper mentions Python and the Kooplearn library but does not provide version numbers for either. |
| Experiment Setup | Yes | For both algorithms each simulation is comprised of 20000 training points, the regularization is γ = 10 4 and the rank is r = 3. Gaussian kernel of length scale 0.175, γ = 10 5 and r = 4. |