Learning Interaction Kernels for Agent Systems on Riemannian Manifolds
Authors: Mauro Maggioni, Jason J Miller, Hongda Qiu, Ming Zhong
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the performance of our estimator on two classical first order interacting systems: Opinion Dynamics and a Predator-Swarm system, with each system constrained on two prototypical manifolds, the 2-dimensional sphere and the Poincar e disk model of hyperbolic space. (...) We conduct extensive experiments on these four scenarios to demonstrate the performance of the estimators both in terms of the estimation errors (approximating φ s) and trajectory estimator errors (estimating the observed dynamics) over [0, T]. |
| Researcher Affiliation | Academia | 1Department of Applied Mathematics & Statistics, Johns Hopkins University 2Department of Mathematics, Department of Applied Mathematics & Statistics, Mathematical Institute for Data Science, Johns Hopkins University. |
| Pseudocode | Yes | Algorithm1 1 shows the detailed steps on how to construct the estimator to φ given the observation data. |
| Open Source Code | Yes | Implementation of the algorithm can be found on https:// github.com/Ming Zhong Codes/Learning Dynamics, which also includes code to reproduce the results presented here. |
| Open Datasets | No | The paper states: "For each system of N = 20 agents, we take M = 500 and L = 500 to generate the training data." However, it does not provide concrete access information (e.g., specific link, DOI, repository name, or formal citation) for this generated training data to be considered publicly available or open. |
| Dataset Splits | No | The paper mentions generating "training data" and evaluating on "new random initial conditions," but it does not explicitly specify training/validation/test dataset splits with percentages, absolute sample counts, or references to predefined splits. |
| Hardware Specification | No | The main paper does not explicitly describe the hardware used for experiments. It mentions in the "Addressing Reviewers Comments" section that "We have added a section, namely Sec. D.1., in the Supplementary Information (SI) to discuss the computing platform used to run the simulations," implying it's not in the main text. |
| Software Dependencies | No | The paper mentions using "a geometric numerical integrator (Hairer, 2001) (4th order Backward Differentiation Formula with a projection scheme)" but does not provide specific version numbers for this or any other software dependencies (e.g., Python, PyTorch, specific libraries). |
| Experiment Setup | Yes | For each system of N = 20 agents, we take M = 500 and L = 500 to generate the training data. For each HM, we use first-degree clamped B-splines as the basis functions with dim(HM) = O(n ) = O(( ML log(ML)) 1 3 ). We use a geometric numerical integrator (Hairer, 2001) (4th order Backward Differentiation Formula with a projection scheme) for the evolution of the dynamics. |