SciML / SciML/NeuralOperators.jl
Implement Koopman Neural Operator (KNO)
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- Dominant language
- Julia
- Stars
- 41
- Forks
- 15
- Avg merge
- 13h 14m
- Merged PRs (30d)
- 12
Description
Summary
Implement KNO, which approximates the Koopman operator to convert nonlinear PDE solving into linear prediction problems.
Reference
- Xiong et al., "Koopman neural operator as a mesh-free solver of non-linear partial differential equations," Journal of Computational Physics, 2024. arXiv:2301.10022
Description
KNO leverages Koopman operator theory: any nonlinear dynamical system can be represented as a linear operator acting on an infinite-dimensional space of observables. KNO learns this linear representation, converting nonlinear PDE solving into linear prediction. The paper presents MLP-based and CNN-based compact variants, plus larger variants built on vision transformers.
This connects naturally to the DynamicalSystems.jl ecosystem and could leverage existing Koopman analysis tools in the SciML ecosystem.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
No file, test, or entry point is named. Start by surveying the existing NeuralOperators.jl implementations and the referenced Koopman analysis tools in the SciML ecosystem, then define the supported KNO variant, API, validation data, and acceptance tests before implementation; done should include a working KNO model with documented behavior and tests.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- julia
- Domain
- machine-learning
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100