Amortized Equation Discovery in Hybrid Dynamical Systems
Authors: Yongtuo Liu, Sara Magliacane, Miltiadis Kofinas, Stratis Gavves
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments on four hybrid and six non-hybrid systems show that our method outperforms previous methods on equation discovery, segmentation, and forecasting. |
| Researcher Affiliation | Academia | 1University of Amsterdam. Correspondence to: Yongtuo Liu <y.liu6@uva.nl>. |
| Pseudocode | No | The paper describes the generative and inference models in detail using mathematical notation and text, but does not include any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | Yes | The code and datasets are available at https://github.com/yongtuoliu/Amortized-Equation Discovery-in-Hybrid-Dynamical-Systems. |
| Open Datasets | Yes | Specifically, we validate on single-object scenarios using the Mass-spring Hopper dataset, and the Susceptible, Infected and Recovered (SIR) disease dataset from Hybrid SINDy (Mangan et al., 2019). We validate on multi-object scenarios using the ODE-driven particle dataset and Salsadancing dataset from GRASS (Liu et al., 2023). Further, we test the robustness of our methods on non-hybrid systems using datasets of the Coupled linear, Cubic oscillator, Lorenz 63, Hopf bifurcation, Seklov glycolysis, and Duffing oscillator from Course & Nair (2023). |
| Dataset Splits | Yes | We scale up the datasets and sample 240 initial conditions from the ranges p0.5, 3q and p 1, 1q for positions a and velocities b, respectively. Among them, 200 samples are for training, 20 for validation, and 20 for testing. (Mass-spring Hopper) ...In summary, 4,928 samples are for training, 191 samples for validation, and 204 samples for testing. (ODE-driven Particle) |
| Hardware Specification | Yes | Each experiment is running on one Nvidia Ge Force RTX 3090 GPU. |
| Software Dependencies | No | The paper mentions using 'Adam optimizer' which implies PyTorch or TensorFlow, but does not provide specific version numbers for any software dependencies like Python, PyTorch, or TensorFlow. |
| Experiment Setup | Yes | We train all datasets with a fixed batch size of 40 for 20,000 training steps. We use the Adam optimizer with 10 5 weight-decay and clip gradients norm to 10. The learning rate is warmed up linearly from 5ˆ10 5 to 2 ˆ 10 4 for the first 2,000 steps, and then decays following a cosine manner with a rate of 0.99. ...dmin and dmax of the count variables are simply set as 20 and 50, respectively for all datasets. The number of edge types L is set as 2, containing one no-interaction type and one with-interaction type. |