Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Probabilistic Exponential Integrators
Authors: Nathanael Bosch, Philipp Hennig, Filip Tronarp
NeurIPS 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate the proposed methods on multiple stiff differential equations and demonstrate their improved stability and efficiency over established probabilistic solvers. (Abstract) and 4 Experiments In this section we investigate the utility and performance of the proposed probabilistic exponential integrators and compare it to standard non-exponential probabilistic solvers on multiple ODEs. |
| Researcher Affiliation | Academia | Nathanael Bosch Tübingen AI Center, University of Tübingen EMAIL Philipp Hennig Tübingen AI Center, University of Tübingen EMAIL Filip Tronarp Lund University EMAIL |
| Pseudocode | No | The paper does not contain a clearly labeled pseudocode or algorithm block. |
| Open Source Code | Yes | Code for the implementation and experiments is publicly available on Git Hub.1 |
| Open Datasets | No | The paper defines the differential equations and their parameters directly within the text and appendix, rather than utilizing external, pre-existing public datasets that require explicit access information. |
| Dataset Splits | No | The paper solves differential equations numerically and does not describe data splitting into training, validation, or test sets in the typical machine learning sense. |
| Hardware Specification | No | All experiments run on a single, consumerlevel CPU. - This statement lacks specific details such as the CPU model, number of cores, or clock speed. |
| Software Dependencies | No | All methods are implemented in the Julia programming language [1]... Reference solutions are computed with the Differential Equations.jl package [34]. - The paper mentions the software used but does not provide specific version numbers for Julia or Differential Equations.jl. |
| Experiment Setup | Yes | We start with a simple one-dimensional initial value problem: a logistic model with negative growth rate parameter r = 1 and carrying capacity K R+, of the form y(t) = y(t) + 1/K y(t)2, t [0, 10], y(0) = 1. (Section 4.1) and We transform the problem into a semi-linear ODE with the method of lines [29, 38], and discretize the spatial domain on 250 equidistant points and approximate the differential operators with finite differences. (Section 4.2) and We again consider a domain Ω= (0, 1), which we discretize on a grid of N = 100 points. (Section 4.3) |