Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
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 | Venue PDF | 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 EMAIL Miguel Liu-Schiaffini Caltech EMAIL Nikola Kovachki NVIDIA EMAIL Burigede Liu University of Cambridge EMAIL Kamyar Azizzadenesheli NVIDIA EMAIL Kaushik Bhattacharya Caltech EMAIL Andrew Stuart Caltech EMAIL Anima Anandkumar Caltech EMAIL |
| 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. |