https://github.com/nathanaelbosch/fenrir.jl
Physics-Enhanced Regression for Initial Value Problems
https://github.com/nathanaelbosch/fenrir.jl
differential-equations hacktoberfest julia odes probabilistic-numerics
Last synced: 4 months ago
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Physics-Enhanced Regression for Initial Value Problems
- Host: GitHub
- URL: https://github.com/nathanaelbosch/fenrir.jl
- Owner: nathanaelbosch
- License: mit
- Archived: true
- Created: 2022-04-05T16:57:09.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2024-02-07T16:48:26.000Z (over 1 year ago)
- Last Synced: 2025-01-20T18:14:12.281Z (4 months ago)
- Topics: differential-equations, hacktoberfest, julia, odes, probabilistic-numerics
- Language: Julia
- Homepage:
- Size: 4.5 MB
- Stars: 19
- Watchers: 5
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
**This package is deprecated and will not be maintained anymore, as the functionality of Fenrir.jl is now implemented in [ProbNumDiffEq.jl](https://github.com/nathanaelbosch/ProbNumDiffEq.jl). Just use [ProbNumDiffEq.jl](https://github.com/nathanaelbosch/ProbNumDiffEq.jl) directy.**
# Fenrir: Physics-Enhanced Regression for IVPs
[](https://nathanaelbosch.github.io/Fenrir.jl/stable)
[](https://nathanaelbosch.github.io/Fenrir.jl/dev)
[](https://github.com/nathanaelbosch/Fenrir.jl/actions/workflows/CI.yml?query=branch%3Amain)
[](https://codecov.io/gh/nathanaelbosch/Fenrir.jl)
This package exports a single function, `fenrir_nll`:
```
fenrir_nll(prob::ODEProblem, data::NamedTuple{(:t, :u)}, observation_noise_var::Real,
diffusion_var::Union{Real,Vector{<:Real}};
adaptive=false, dt=false, proj=I, order=3::Int, tstops=[])
Compute the "Fenrir" approximate negative log-likelihood (NLL) of the data.
```
To see the full docstring, check out the
[documentation](https://nathanaelbosch.github.io/Fenrir.jl/stable).
### Minimal example: Parameter likelihood on FitzHugh-Nagumo
```julia
using ProbNumDiffEq, Plots, LinearAlgebra, Fenrir
# Define problem:
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)
# Generate data:
true_sol = solve(prob, EK1())
times = 1:0.1:20
odedata = [u + 0.1*randn(size(u)) for u in true_sol(times).u.μ]
scatter(times, ProbNumDiffEq.stack(odedata), markersize=2, markerstrokewidth=0.1,
color=1, label=["Data" ""])
# With the wrong parameters:
pwrong = (0.1, 0.1, 2.0)
solwrong = solve(remake(prob, p=pwrong), EK1(smooth=false), dense=false);
plot!(solwrong, color=2, label=["Wrong solution" ""])
# Fenrir:
data = (t=times, u=odedata);
σ² = 1e-1
κ² = 1e30
nll, ts, states = fenrir_nll(remake(prob, p=pwrong), data, σ², κ²)
means = ProbNumDiffEq.stack([x.μ for x in states]);
stddevs = ProbNumDiffEq.stack([sqrt.(diag(x.Σ)) for x in states]);
plot!(ts, means, ribbon=2stddevs,
marker=:o, markersize=1, markerstrokewidth=0.1,
color=3, fillalpha=0.1, label=["Fenrir interpolation" ""])
println("Negative log-likelihood: $nll")
```
Prints: `Negative log-likelihood: 5849.3096741464615`
You can use this NLL it as any other NLL:
Optimize it to compute maximum-likelihood estimates or MAPs,
or plug it into MCMC to sample from the posterior.
In [our paper](https://arxiv.org/abs/2202.01287) we compute MLEs by pairing Fenrir with [Optimization.jl](http://optimization.sciml.ai/stable/) and [ForwardDiff.jl](https://juliadiff.org/ForwardDiff.jl/stable/).
Check out the [documentation](https://nathanaelbosch.github.io/Fenrir.jl/stable/) for more details on how to do this.
## Reference
This method has been developed in the paper "Fenrir: Physics-Enhanced Regression for Initial Value Problems" by Tronarp et al, published at ICML 2022 ([link](https://proceedings.mlr.press/v162/tronarp22a.html)).
```
@InProceedings{pmlr-v162-tronarp22a,
title = {Fenrir: Physics-Enhanced Regression for Initial Value Problems},
author = {Tronarp, Filip and Bosch, Nathanael and Hennig, Philipp},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {21776--21794},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/tronarp22a/tronarp22a.pdf},
url = {https://proceedings.mlr.press/v162/tronarp22a.html}
}
```