Probabilistic Exponential Integrators
Authors: Nathanael Bosch, Philipp Hennig, Filip Tronarp
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | 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 nathanael.bosch@uni-tuebingen.de Philipp Hennig Tübingen AI Center, University of Tübingen philipp.hennig@uni-tuebingen.de Filip Tronarp Lund University filip.tronarp@matstat.lu.se |
| 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) |