Fenrir: Physics-Enhanced Regression for Initial Value Problems
Authors: Filip Tronarp, Nathanael Bosch, Philipp Hennig
ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | This section investigates the utility and performance of Fenrir in a range of numerical experiments. It is structured as follows. Section 5.1 evaluates Fenrir on two standard benchmark problems. Section 5.2 demonstrates the utility of the proposed marginal likelihood for model selection. Section 5.3 considers systems with only partially observable states and shows that Fenrir, unlike most gradient matching methods, is still applicable. Finally, Section 5.4 investigates highly oscillatory systems which present a particular challenge for numerical integration-based methods. |
| Researcher Affiliation | Academia | 1Department of Computer Science, University of T ubingen, T ubingen, Germany 2Max Planck Institute for Intelligent Systems, T ubingen, Germany. |
| Pseudocode | No | The paper describes methods using mathematical equations and text, but does not include structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Code is publicly available on Git Hub.2 https://github.com/nathanaelbosch/ fenrir-experiments |
| Open Datasets | Yes | This experiment evaluates Fenrir on two benchmark problems that have been extensively studied in the both the gradient matching and the numerical integration literature (Calderhead et al., 2009; Wenk et al., 2020), namely the Lotka Volterra predator-prey model and the Fitz Hugh Nagumo neuronal model. |
| Dataset Splits | No | The paper describes data generation and noise addition for experiments (e.g., 'noisy observations are drawn from the numerically computed, true system trajectories'), but does not explicitly provide information on standard training, validation, or testing dataset splits. |
| Hardware Specification | No | All experiments run on a single, consumer-level CPU. |
| Software Dependencies | No | All experiments are implemented in the Julia programming language (Bezanson et al., 2017). Runge Kutta reference solutions are computed with Differential Equations.jl (Rackauckas & Nie, 2017), and numerical optimizers are provided by Optim.jl (Mogensen & Riseth, 2018). (Specific version numbers for libraries like DifferentialEquations.jl and Optim.jl are not provided.) |
| Experiment Setup | Yes | In all experiment, the observation noise σ2 and the diffusion κ are optimised in log-space... All parameters are optimised jointly by Fenrir via L-BFGS, with bounds for parameters and initial values chosen as in Appendix C.2... Finally, a step-size of = 5 10 3 is chosen for Fenrir s probabilistic numerical integration. |