Sparse Learning of Dynamical Systems in RKHS: An Operator-Theoretic Approach
Authors: Boya Hou, Sina Sanjari, Nathan Dahlin, Subhonmesh Bose, Umesh Vaidya
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this work, we present a method for sparse learning of transfer operators from βmixing stochastic processes, in both discrete and continuous time, and provide sample complexity analysis extending existing theoretical guarantees for learning from non-sparse, i.i.d. data. In addressing continuous-time settings, we develop precise descriptions using covariance-type operators for the infinitesimal generator that aids in the sample complexity analysis. We empirically illustrate the efficacy of our sparse embedding approach through deterministic and stochastic nonlinear system examples. |
| Researcher Affiliation | Academia | 1Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA 2Department of Mechanical Engineering, Clemson University, Clemson SC, 29634, USA. Correspondence to: Boya Hou <boyahou2@illinois.edu>. |
| Pseudocode | Yes | Algorithm 1 Sample-based Sparse Learning of A Without Explicit Knowledge of SDE Coefficients |
| Open Source Code | No | The paper does not provide an explicit statement about releasing source code or a link to a code repository for the methodology described. |
| Open Datasets | No | The paper describes generating datasets for the experiments (e.g., 'we sample 100 trajectories to form D1 by first generating 100 uniformly distributed initial points from [−2, 2] × [−2, 2]', 'create a dataset D from 10 trajectories with 5000 evaluations each'), but it does not provide access information (like a URL, DOI, or specific citation) for a publicly available or open dataset. |
| Dataset Splits | No | The paper describes data generation and sub-sampling, but it does not specify explicit training, validation, or test dataset splits or mention cross-validation. For example, in Section 9.1: 'D2 is constructed from 50 uniformly distributed initial points with 100 evaluations along each and then sub-sampled with m = 20, s = 5 for each trajectory.' |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments (e.g., GPU/CPU models, memory specifications). |
| Software Dependencies | No | The paper mentions methods like 'Euler-Maruyama method (Higham, 2001)' but does not specify any software dependencies with version numbers (e.g., Python 3.x, PyTorch 1.x). |
| Experiment Setup | Yes | The paper provides detailed experimental setup for numerical experiments, including sampling intervals, number of trajectories, initial points, sub-sampling parameters, and kernel types. For example, in Section 9.1: 'To approximate A, we sample 100 trajectories to form D1 by first generating 100 uniformly distributed initial points from [−2, 2] × [−2, 2], then propagating them through the dynamics by evolving 1000 steps with sampling interval τ = 0.01 s. We then create a sub-sample with m = 200, and s = 5 along each trajectory. We utilize a Gaussian kernel κ(x1, x2) = exp(−‖x1 − x2‖2/(2σ2)), whose partial derivatives are included in Appendix N. Setting γ1 = 0.992, we get |Dγ1| = 1477.' |