Physics-informed Spline Learning for Nonlinear Dynamics Discovery
Authors: Fangzheng Sun, Yang Liu, Hao Sun
IJCAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The efficacy and superiority of the proposed method have been demonstrated by multiple wellknown nonlinear dynamical systems, in comparison with two state-of-the-art methods. ... In this section, we evaluate the efficacy of Pi SL in the discovery of governing equations for two nonlinear chaotic dynamical systems based on sparsely sampled synthetic noisy data ... We also compare the performance of our approach with two open source state-of-art models ... The robustness of Pi SL against different levels of data noise is analyzed. The discovered equations are further validated on different datasets ... |
| Researcher Affiliation | Academia | 1 Department of Civil and Environmental Engineering, Northeastern University, Boston, MA, USA 2 Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA 3 Department of Civil and Environmental Engineering, MIT, Cambridge, MA, USA |
| Pseudocode | Yes | Algorithm 1: Hybrid ADO Strategy ... Algorithm 2: STRidge |
| Open Source Code | Yes | Source codes/datasets are available on Git Hub at https://github. com/isds-neu/Pi SL upon final publication. |
| Open Datasets | No | The synthetic datasets are generated by solving nonlinear differential equation by the Matlab ode113 function. ... We generate the noisy sub-sampled datasets under four different ICs as measurements ... We measure these trajectories (e.g., by video camera in practice) for 2 seconds with a sampling rate of 800 Hz and then transform back to angular time histories as measurement data for discovery. |
| Dataset Splits | No | The paper discusses 'validation' of the discovered equations on different initial conditions (ICs) but does not provide specific details on training/validation/test dataset splits used for model development or hyperparameter tuning. |
| Hardware Specification | Yes | All simulations in this paper are performed on a NVIDIA Ge Force RTX 2080Ti GPU in a workstation with 8 Intel Core i9-9900K CPUs. |
| Software Dependencies | No | The proposed computational framework is implemented in Py Torch to leverage the power of graph-based GPU computing. However, no specific version number for PyTorch or any other software dependencies is provided. |
| Experiment Setup | No | The paper describes the general optimization strategy (pre-training, ADO, post-tuning) and provides criteria for selecting some hyperparameters (e.g., 'η is a small number (e.g., 10 6)', 'α follows the scale ratio between state and its derivative'). However, it does not provide concrete numerical values for common training hyperparameters such as learning rate, batch size, or specific epoch counts for the Pi SL method itself. |