This repo contains the experiment code for the paper "Fenrir: Physics-Enhanced Regression for Initial Value Problems", accepted at ICML 2022 (link).
The functionality of this paper is available in Fenrir.jl. If you want to use the new PN marginal likelihood for an inference problem, we recommend to use Fenrir.jl and not this repo.
If you want to solve differential equations with probabilistic numerical solvers, have a look at ProbNumDiffEq.jl.
It contains fast ODE filters for first- and second-order ODEs, and even DAEs.
And if you prefer Python, just use one of the many solvers implemented in ProbNum (pip install probnum).
The experiments are located in ./experiments/; each subfolder has an individual README that explains the individual files.
Since the scripts use the core located in ./src/, code should be run from the root directory directly.
First open julia, activate the local environment, and instantiate it to install all the packages:
julia> ]
(v1.7) pkg> activate .
(v1.7) pkg> instantiate
and you can quit the pkg environment by hitting backspace.
To run a julia script from the Julia REPL, say ./experiments/2/plot.jl, do
julia> include("experiments/2/plot.jl")
(link)
@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}
}