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 and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems
Authors: Minchan Jeong, Jongha (Jon) Ryu, Se-Young Yun, Gregory Wornell
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirical results demonstrate that the learned singular subspaces are both reliable and effective for downstream tasks such as eigen-analysis and multi-step prediction. (...) 4 Experiments We demonstrate the efficacy of the proposed techniques using the experimental suite of [16]. Unless stated otherwise, all experimental settings are mostly identical to those in [16] except the molecular dynamics experiment. All technical details and configurations are provided in Appendix G. The appendix also includes an additional experiment on an instance of a 1D noisy logistic map, whose Koopman operator has finite rank. We defer this result to the appendix, as most methods perform comparably in this simple setting. |
| Researcher Affiliation | Academia | 1Kim Jaechul Graduate School of AI, KAIST, Daejeon 34141, South Korea 2Department of EECS, MIT, Cambridge, MA 02139, United States EMAIL, EMAIL |
| Pseudocode | Yes | F.2 Pseudocode for Lo RA Loss with Nesting Based on the nesting techniques described above, here we provide a simple and efficient Py Torch [30] implementation of the Nested Lo RA (i.e., Lo RA with nesting) objective. 1 class Nested Lo RALoss: 2 def __init__( |
| Open Source Code | Yes | Our Py Torch [30] implementation is publicly available at https: //github.com/Minchan Jeong/Neural Koopman SVD. |
| Open Datasets | Yes | 4.1 Ordered MNIST We considered the ordered MNIST example, a synthetic experiment which was first considered in [14]: (...) 4.3 Chignolin Molecular Dynamics To assess scalability on high-dimensional data, we apply our method to the analysis of chignolin molecular dynamics. Chignolin is an artificial mini-protein that is considered a standard model for studying rapid folding dynamics due to its complex and fast transitions [20, 3, 16]. The underlying physical system is time-reversible, and thus the Koopman operator is self-adjoint. The slowest decay mode in chignolin is associated with the folding-unfolding transition, which occurs on a microsecond timescale [20]. Unlike [16], we use the public dataset of [25]. |
| Dataset Splits | Yes | G.2 Ordered MNIST Following the setup of [16], we generated two independent trajectories of length 1000. We used one trajectory for training and the other for evaluation. (...) G.4 Chignolin Molecular Dynamics To mitigate this distribution shift and decouple data sampling variance from optimization variance, we employed a distribution-matching split strategy. Specifically, we generated 200 candidate stratified splits and selected the partition that minimizes the 1-Wasserstein distance between the training and test set distributions of the radius of gyration, computed using the 10 CĪ± atoms. To ensure balanced initial conditions, we further constrained the split such that the 17 folded-initiated and 17 unfolded-initiated trajectories were each divided into 13 training and 4 testing trajectories. |
| Hardware Specification | Yes | G.5 Computing Resources All experiments were conducted on a server equipped with two Intel(R) Xeon(R) Gold 5220R CPUs, about 500 Gi B of total RAM, four NVIDIA A5000 GPUs, and a 1TB NVMe SSD for storage. |
| Software Dependencies | Yes | All experiments utilized Py Torch; the chignolin simulations additionally employed Sch Net Pack 2.1.1 [35]. |
| Experiment Setup | Yes | G.2 Ordered MNIST Following the setup of [16], we generated two independent trajectories of length 1000. We used one trajectory for training and the other for evaluation. We used Adam optimizer with learning rate 10^-3, batch size 64, for 100 epochs. The convolutional neural network we used is same as [16], namely, Conv2d[16] ReLU Max Pool[2] Conv2d[32] ReLU Max Pool[2] Linear[10]. We set the metric deformation loss coefficient to be 1 as suggested for DPNet and DPNet-relaxed. (...) G.3 Langevin Dynamics We parameterized the top-10 eigenfunctions using a single MLP with hidden units 128-128-128 and CeLU activation. We trained the network using Adam optimizer with learning rate 10^-3 for 50,000 iterations with batch size 128. Exponential moving average with decay 0.995 was applied to result in a smoother result. (...) G.4 Chignolin Molecular Dynamics Therefore, we trained the models for 100 epochs with the Adam optimizer whose learning rate is 10^-3, but doubled the batch size to 384 to maximize GPU memory utilization. We also used Ī³ = 0.01 for the regularization coefficient of DPNet-relaxed. The Sch Net architecture used in our experiments is summarized in Table 4. |