Training neural operators to preserve invariant measures of chaotic attractors
Authors: Ruoxi Jiang, Peter Y. Lu, Elena Orlova, Rebecca Willett
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | On a variety of chaotic systems, our method is shown empirically to preserve invariant measures of chaotic attractors. We evaluate our approach on the 1D chaotic Kuramoto Sivanshinsky (KS) system and a finite-dimensional Lorenz 96 system. In all cases, we ensure that the systems under investigation remain in chaotic regimes. We demonstrate the effectiveness of our approach in preserving key statistics in these unpredictable systems, showcasing our ability to handle the complex nature of chaotic systems. |
| Researcher Affiliation | Academia | Ruoxi Jiang Department of Computer Science University of Chicago Chicago, IL 60637 roxie62@uchicago.edu Peter Y. Lu Department of Physics University of Chicago Chicago, IL 60637 lup@uchicago.edu Elena Orlova Department of Computer Science University of Chicago Chicago, IL 60637 eorlova@uchicago.edu Rebecca Willett Department of Statistics and Computer Science University of Chicago Chicago, IL 60637 willett@uchicago.edu |
| Pseudocode | No | The paper does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | The code is available at: https://github.com/roxie62/neural_operators_for_chaos. |
| Open Datasets | No | Our data consists of noisy observations u(t) with noise η N(0, r2σ2I), where σ2 is the temporal variance of the trajectory and r is a scaling factor. We generate 2000 training data points with each ϕ(n) randomly sampled from a uniform distribution with the range [10.0, 18.0]. We discretize these training trajectories into time steps of dt = 0.1 over a total time of t = 205s, yielding 2050 discretized time steps. The paper describes how to *generate* the data rather than providing a link to an existing dataset or a hosted version of their generated data. |
| Dataset Splits | No | From our observations during the validation phase, we noted that the feature loss was at its lowest with an acceptable RMSE (which is lower than 110% compared to the baseline) when λ = 0.8. The paper mentions a 'validation phase' but does not specify the dataset split percentages or sample counts for training, validation, and test sets. |
| Hardware Specification | No | Training time (minutes) with 4 GPUs for 60-dimensional Lorenz-96 and 256-dimensional Kuramoto Sivashinsky. The paper mentions the number of GPUs but does not specify the exact model or any other hardware components like CPU or memory. |
| Software Dependencies | No | We adapted the Julia Dynamical System.jl package to calculate the leading LE. We use the Julia Dynamical System.jl package for calculating the fractal dimension. The paper mentions specific software packages (e.g., 'Julia Dynamical System.jl') but does not provide version numbers for these or other relevant software dependencies like Python, PyTorch, etc. |
| Experiment Setup | Yes | We determine the roll-out step during training (i.e., h and h RMSE) via the grid search from the set of values {1, 2, 3, 4, 5}. ... For the experiments conducted using Lorenz-96, we selected α = 3 and γ = 0.02. ... we set λ at 0.8. We use the Res Net-34 as the backbone of the encoder, throughout all experiments, we train the encoder using the Adam W optimization algorithm [52], with a weight decay of 10 5, and set the training duration to 2000 epochs. For the temperature value τ... we start with a relatively low τ value (0.3 in our experiments) for the first 1000 epochs. ... Subsequently, we incrementally increase τ up to a specified value (0.7 in our case)... In our experiment, we set α = 3 and γ = 0.05. |