ProbNumDiffEq.jl
ProbNumDiffEq.jl: Probabilistic Numerical Solvers for Ordinary Differential Equations in Julia - Published in JOSS (2024)
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Published in Journal of Open Source Software
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Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing
Basic Info
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- Stars: 129
- Watchers: 4
- Forks: 16
- Open Issues: 16
- Releases: 68
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Metadata Files
README.md
ProbNumDiffEq.jl
ProbNumDiffEq.jl provides probabilistic numerical ODE solvers to the DifferentialEquations.jl ecosystem. The implemented ODE filters solve differential equations via Bayesian filtering and smoothing. The filters compute not just a single point estimate of the true solution, but a posterior distribution that contains an estimate of its numerical approximation error.
For a short intro video, check out the ProbNumDiffEq.jl poster presentation at JuliaCon2021.
Installation
Run Julia, enter ] to bring up Julia's package manager, and add the ProbNumDiffEq.jl package:
julia> ]
(v1.8) pkg> add ProbNumDiffEq
Example: Solving the FitzHugh-Nagumo ODE
```julia using ProbNumDiffEq
ODE definition as in DifferentialEquations.jl
function f(du, u, p, t) a, b, c = p du[1] = c * (u[1] - u[1]^3 / 3 + u[2]) du[2] = -(1 / c) * (u[1] - a - b * u[2]) end u0 = [-1.0, 1.0] tspan = (0.0, 20.0) p = (0.2, 0.2, 3.0) prob = ODEProblem(f, u0, tspan, p)
Solve the ODE with a probabilistic numerical solver: EK1
sol = solve(prob, EK1())
Plot the solution with Plots.jl
using Plots plot(sol, color=["#CB3C33" "#389826" "#9558B2"]) ```
In probabilistic numerics, the solution also contains error estimates - it just happens that they are too small to be visible in the plot above. But we can just plot them directly:
julia
using Statistics
stds = std.(sol.pu)
plot(sol.t, hcat(stds...)', color=["#CB3C33" "#389826" "#9558B2"],
label=["std(u1(t))" "std(u2(t))"], xlabel="t", ylabel="standard-deviation")
Contributing
Contributions are very welcome! Check the existing issues for ideas on how to contribute to the package. If you want to implement a new functionality/algorithm, open an issue to start a discussion.
Please open issues liberally! If there is anything that's unclear or doesn't work, we would very much like to know about it. This includes not just bugs and feature requests but also general questions about the software, feedback and suggestions.
Citing ProbNumDiffEq.jl
If you use ProbNumDiffEq.jl helpful for your research project, please cite our JOSS paper (link):
@article{Bosch2024,
doi = {10.21105/joss.07048},
url = {https://doi.org/10.21105/joss.07048},
year = 2024,
publisher = {The Open Journal},
volume = 9,
number = 101,
pages = 7048,
author = {Nathanael Bosch},
title = {ProbNumDiffEq.jl: Probabilistic Numerical Solvers for Ordinary
Differential Equations in Julia},
journal = {Journal of Open Source Software}
}
Related packages
- ProbDiffEq is similar in scope to ProbNumDiffEq.jl and it provides fast and feature-rich probabilistic ODE solvers but is implemented in Python and built on JAX.
- ProbNum implements a wide range of probabilistic numerical methods, not only for ODEs but also for linear algebra, quadrature, and filtering/smoothing. It is implemented in Python and NumPy, and it focuses more on breadth and didactic purposes than on performance.
Owner
- Name: Nathanael Bosch
- Login: nathanaelbosch
- Kind: user
- Location: Tübingen, Germany
- Company: University of Tübingen
- Website: nathanaelbosch.github.io
- Twitter: nathanaelbosch
- Repositories: 43
- Profile: https://github.com/nathanaelbosch
PhD student at Uni Tübingen, working on machine learning and probabilistic numerics.
JOSS Publication
ProbNumDiffEq.jl: Probabilistic Numerical Solvers for Ordinary Differential Equations in Julia
Authors
Tübingen AI Center, University of Tübingen, Germany
Editor
Mehmet Hakan Satman
Tags
probabilistic numerics differential equations Bayesian filtering and smoothing simulationCitation (CITATION.cff)
cff-version: 1.2.0 message: "If you use this software, please it as below." authors: - family-names: "Bosch" given-names: "Nathanael" orcid: "https://orcid.org/0000-0003-0139-4622" title: 'ProbNumDiffEq.jl: Probabilistic Numerical Solvers for Ordinary Differential Equations in Julia' version: 0.16.2 doi: 10.21105/joss.07048 date-released: '2024-10-01' url: https://doi.org/10.21105/joss.07048
GitHub Events
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- Create event: 12
- Commit comment event: 4
- Release event: 2
- Issues event: 2
- Watch event: 9
- Delete event: 10
- Issue comment event: 35
- Push event: 59
- Pull request review event: 4
- Pull request review comment event: 5
- Pull request event: 31
- Fork event: 1
Last Year
- Create event: 12
- Commit comment event: 4
- Release event: 2
- Issues event: 2
- Watch event: 9
- Delete event: 10
- Issue comment event: 35
- Push event: 59
- Pull request review event: 4
- Pull request review comment event: 5
- Pull request event: 31
- Fork event: 1
Committers
Last synced: 5 months ago
Top Committers
| Name | Commits | |
|---|---|---|
| Nathanael Bosch | n****h@t****e | 861 |
| github-actions[bot] | 4****] | 104 |
| Nathanael Bosch | n****h@g****e | 43 |
| dependabot[bot] | 4****] | 5 |
| Christopher Rackauckas | a****s@c****m | 3 |
| Pietro Monticone | 3****e | 2 |
| Cornelius Roemer | c****r@g****m | 1 |
| Daniel González Arribas | d****s@g****m | 1 |
| David Widmann | d****n | 1 |
| Jadon Clugston | 3****r | 1 |
| Jose Storopoli | 4****i | 1 |
| Qingyu Qu | 5****Y | 1 |
| Tim Holy | t****y@g****m | 1 |
| Vedant Puri | v****i@g****m | 1 |
| CompatHelper Julia | c****y@j****g | 1 |
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Issues and Pull Requests
Last synced: 4 months ago
All Time
- Total issues: 34
- Total pull requests: 189
- Average time to close issues: 3 months
- Average time to close pull requests: 12 days
- Total issue authors: 11
- Total pull request authors: 11
- Average comments per issue: 3.35
- Average comments per pull request: 1.07
- Merged pull requests: 175
- Bot issues: 0
- Bot pull requests: 57
Past Year
- Issues: 3
- Pull requests: 30
- Average time to close issues: 2 days
- Average time to close pull requests: 16 days
- Issue authors: 3
- Pull request authors: 6
- Average comments per issue: 2.0
- Average comments per pull request: 1.97
- Merged pull requests: 21
- Bot issues: 0
- Bot pull requests: 12
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- nathanaelbosch (23)
- ranocha (2)
- ChrisRackauckas (1)
- lazarusA (1)
- vboddeti (1)
- jnsbck (1)
- TheFibonacciEffect (1)
- PieterjanRobbe (1)
- sdwfrost (1)
- rolson24 (1)
- JuliaTagBot (1)
Pull Request Authors
- nathanaelbosch (134)
- github-actions[bot] (60)
- dependabot[bot] (8)
- ChrisRackauckas (5)
- jbytecode (2)
- pitmonticone (2)
- jClugstor (2)
- vpuri3 (1)
- devmotion (1)
- DaniGlez (1)
- timholy (1)
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- Total packages: 1
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Total downloads:
- julia 2 total
- Total dependent packages: 1
- Total dependent repositories: 0
- Total versions: 67
juliahub.com: ProbNumDiffEq
Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing
- Documentation: https://docs.juliahub.com/General/ProbNumDiffEq/stable/
- License: MIT
-
Latest release: 0.16.4
published 5 months ago
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