Learning Chaotic Dynamics in Dissipative Systems
Authors: Zongyi Li, Miguel Liu-Schiaffini, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate our approach on the finite-dimensional, chaotic Lorenz-63 system as well as the chaotic 1D Kuramoto-Sivashinsky and 2D Navier-Stokes equations. In all cases we show that encouraging dissipativity is crucial for capturing the global attractor and evaluating statistics of the invariant measure. |
| Researcher Affiliation | Collaboration | Caltech zongyili@caltech.edu Miguel Liu-Schiaffini Caltech mliuschi@caltech.edu Nikola Kovachki NVIDIA nkovachki@nvidia.com Burigede Liu University of Cambridge bl377@eng.cam.ac.uk Kamyar Azizzadenesheli NVIDIA kamyara@nvidia.com Kaushik Bhattacharya Caltech bhatta@caltech.edu Andrew Stuart Caltech astuart@caltech.edu Anima Anandkumar Caltech anima@caltech.edu |
| Pseudocode | No | No pseudocode or clearly labeled algorithm block is present in the paper. |
| Open Source Code | Yes | The code is available at https://github.com/neural-operator/markov_neural_operator |
| Open Datasets | No | The paper uses data generated from well-known chaotic systems (Lorenz-63, Kuramoto-Sivashinsky, Navier-Stokes/Kolmogorov Flow) and describes parameters for these systems, but it does not provide a link, DOI, or formal citation for the specific dataset (trajectories) they used for training, validation, or testing. |
| Dataset Splits | No | The paper does not explicitly provide specific training, validation, or test dataset split percentages or sample counts. It mentions training on a single trajectory for Lorenz-63 but not specific splits. |
| Hardware Specification | No | The paper does not explicitly describe the specific hardware used for running experiments, such as GPU models, CPU types, or memory specifications. |
| Software Dependencies | No | The paper does not provide specific version numbers for key software components or libraries (e.g., Python, PyTorch, TensorFlow, specific solvers) needed to reproduce the experiments. |
| Experiment Setup | Yes | We use the canonical parameters ( , b, r) = (10, 8/3, 28) [51]. Since the solution operator of the Lorenz-63 system is finite-dimensional, we learn it by training a feedforward neural network on a single trajectory with h = 0.05s on the Lorenz attractor. We encourage dissipativity during training with the criterion described in eq. (7), with λ = 0.5 and being a uniform probability distribution supported on a shell around the origin. |