https://github.com/uqatkit/eikonax
A Fully Differentiable Solver for the Anisotropic Eikonal Equation
Science Score: 26.0%
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Keywords
Repository
A Fully Differentiable Solver for the Anisotropic Eikonal Equation
Basic Info
- Host: GitHub
- Owner: UQatKIT
- License: mit
- Language: Python
- Default Branch: main
- Homepage: https://uqatkit.github.io/Eikonax/
- Size: 5.17 MB
Statistics
- Stars: 3
- Watchers: 1
- Forks: 0
- Open Issues: 5
- Releases: 17
Topics
Metadata Files
README.md
Eikonax: A Fully Differentiable Solver for the Anisotropic Eikonal Equation
Eikonax is a pure-Python implementation of a solver for the anisotropic eikonal equation on triangulated meshes. In particular, it focuses on domains $\Omega$ either in 2D Euclidean space, or 2D manifolds in 3D Euclidean space. For a given, space-dependent parameter tensor field $\mathbf{M}$, and a set $\Gamma$ of initially active points, Eikonax computes the arrival times $u$ according to
$$ \begin{gather} \sqrt{\big(\nabla u(\mathbf{x}),\mathbf{M}(\mathbf{x})\nabla u(\mathbf{x})\big)} = 1,\quad \mathbf{x}\in\Omega, \ \nabla u(\mathbf{x}) \cdot \mathbf{n}(\mathbf{x}) \geq 0,\quad \mathbf{x}\in\partial\Omega, \ u(\mathbf{x}0) = u0,\quad \mathbf{x}_0 \in \Gamma. \end{gather} $$
The iterative solver is based on Godunov-type upwinding and employs global Jacobi updates, which can be efficiently ported to SIMD architectures. In addition, Eikonax implements an efficient algorithm for the evaluation of parametric derivatives, meaning the derivative of the solution vector with respect to the parameter tensor field, $\frac{du}{d\mathbf{M}}$. More precisely, we assume that the tensor field is parameterized through some vector $\mathbf{m}$, s.th. we compute $\frac{du}{d\mathbf{m}} = \frac{du}{d\mathbf{M}}\frac{d\mathbf{M}}{d\mathbf{m}}$. This make Eikonax particularly suitable for the inverse problem setting, where derivative information is typically indispensable for efficient solution procedures. Through exploitation of causality in the forward solution, Eikonax can compute these derivatives through discrete adjoints on timescales much smaller than those for the forward solve.
Key Features
- Supports anisotropic conductivity tensors
- Works on irregular meshes
- GPU offloading of performance-relevant computations
- Super fast derivatives through causality-informed adjoints
Eikonax is mainly based on the JAX software library. This allows for GPU offloading of relevant computations. In addition, Eikonax makes extensive use of JAX`s just-in-time compilation and automatic differentiation capabilities.
Getting Started
Eikonax is deployed as a python package, simply install via
bash
pip install eikonax
For development, we recommend using the great uv project management tool, for which Eikonax provides a universal lock file. To set up a reproducible environment, run
bash
uv sync --all-groups
in the project root directory.
Documentation
The documentation provides further information regarding usage, theoretical background, technical setup and API. Alternatively, you can check out the notebooks under examples
Acknowledgement and License
Eikonax is being developed in the research group Uncertainty Quantification at KIT. It is partially based on the excellent FIM-Python tool. Eikonax is distributed as free software under the MIT License.
Owner
- Name: Uncertainty Quantification Research Group at KIT
- Login: UQatKIT
- Kind: organization
- Location: Germany
- Website: https://www.scc.kit.edu/forschung/uq
- Repositories: 1
- Profile: https://github.com/UQatKIT
GitHub Events
Total
- Create event: 32
- Issues event: 13
- Release event: 23
- Watch event: 4
- Delete event: 17
- Issue comment event: 1
- Member event: 1
- Push event: 120
- Pull request event: 3
Last Year
- Create event: 32
- Issues event: 13
- Release event: 23
- Watch event: 4
- Delete event: 17
- Issue comment event: 1
- Member event: 1
- Push event: 120
- Pull request event: 3
Issues and Pull Requests
Last synced: 10 months ago
All Time
- Total issues: 10
- Total pull requests: 2
- Average time to close issues: 5 days
- Average time to close pull requests: less than a minute
- Total issue authors: 1
- Total pull request authors: 1
- Average comments per issue: 0.0
- Average comments per pull request: 0.0
- Merged pull requests: 1
- Bot issues: 0
- Bot pull requests: 0
Past Year
- Issues: 10
- Pull requests: 2
- Average time to close issues: 5 days
- Average time to close pull requests: less than a minute
- Issue authors: 1
- Pull request authors: 1
- Average comments per issue: 0.0
- Average comments per pull request: 0.0
- Merged pull requests: 1
- Bot issues: 0
- Bot pull requests: 0
Top Authors
Issue Authors
- maximilian-kruse (9)
Pull Request Authors
- maximilian-kruse (2)
Top Labels
Issue Labels
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Packages
- Total packages: 1
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Total downloads:
- pypi 383 last-month
- Total dependent packages: 0
- Total dependent repositories: 0
- Total versions: 13
- Total maintainers: 1
pypi.org: eikonax
Differentiable Solver for the Anisotropic Eikonal Equation on Triangulated Meshes
- Documentation: https://eikonax.readthedocs.io/
- License: MIT
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Latest release: 0.3.2
published 10 months ago
Rankings
Maintainers (1)
Dependencies
- beartype >=0.19.0,<0.20
- equinox >=0.11.5,<0.11.6
- jax >=0.4.31,<0.5
- jaxtyping >=0.2.36,<0.3
- numpy >=2.1.1,<3
- scipy >=1.14.1,<2
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- 155 dependencies