ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residuals
Authors: Yuanchao Xu, Kaidi Shao, Nikos K. Logothetis, Zhongwei Shen
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments on a variety of physical and biological systems show that Res Koop Net achieves more accurate spectral approximations than existing methods, particularly for high-dimensional systems and those with continuous spectra, which demonstrates its effectiveness as a tool for analyzing complex dynamical systems. Our turbulence analysis demonstrates Res Koop Net's ability to detect not only acoustic vibration and turbulent fluctuation... In the neural dynamics example, we compare against three methods across five mice datasets... |
| Researcher Affiliation | Academia | 1Department of Mathematical and Statistical Science, University of Alberta, Edmonton, Canada 2International Center for Primate Brain Research, Chinese Academy of Sciences, Shanghai, China. Correspondence to: Zhongwei Shen <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Res Koop Net |
| Open Source Code | Yes | For reproducibility, the source code is available at this link. |
| Open Datasets | Yes | The turbulent flow dataset from Colbrook & Townsend (2024, Section 6.3)... The dataset is part of the open dataset on mice from the competition Sensorium 2023 (Turishcheva et al., 2024b;a). |
| Dataset Splits | No | Neural dynamics: We trained dictionaries on all snapshots from each mouse to avoid overfitting. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. It only mentions 'computational demands' generically. |
| Software Dependencies | No | We use the hyperbolic tangent (tanh) function as the activation function for the hidden layers and employ the Adam optimizer for updating the network parameters θ. The paper mentions software components but does not provide specific version numbers for them. |
| Experiment Setup | Yes | We choose 3 hidden layers and use 300 neurons and 350 neuron in each hidden layer in both cases, respectively. The neural network we use here consists of 3 hidden layers, each with 200 neurons. The hyperparameter scanning results are included in Appendix Figure 17. |