Inferring microscale properties of interacting systems from macroscale observations

Campioni, N., Husmeier, D. , Morales, J. , Gaskell, J. and Torney, C. J. (2021) Inferring microscale properties of interacting systems from macroscale observations. Physical Review Research, 3(4), 043074. (doi: 10.1103/PhysRevResearch.3.043074)

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Emergent dynamics of complex systems are observed throughout nature and society. The coordinated motion of bird flocks, the spread of opinions, fashions and fads, or the dynamics of an epidemic, are all examples of complex macroscale phenomena that arise from fine-scale interactions at the individual level. In many scenarios, observations of the system can only be made at the macroscale, while we are interested in creating and fitting models of the microscale dynamics. This creates a challenge for inference as a formal mathematical link between the microscale and macroscale is rarely available. Here, we develop an inferential framework that bypasses the need for a formal link between scales and instead uses sparse Gaussian process regression to learn the drift and diffusion terms of an empirical Fokker-Planck equation, which describes the time evolution of the probability density of a macroscale variable. This gives us access to the likelihood of the microscale properties of the physical system and a second Gaussian process is then used to emulate the log-likelihood surface, allowing us to define a fast, adaptive MCMC sampler, which iteratively refines the emulator when needed. We illustrate the performance of our method by applying it to a simple model of collective motion.

Item Type:Articles
Additional Information:This work was supported by the Leverhulme Foundation (RPG-2018-398). JMM was supported by a Leverhulme Visiting Professorship (VP2-2018-0630). CJT is supported by a James S. McDonnell Foundation Studying Complex Systems Scholar Award. DH is supported by the Engineering and Physical Sciences Research Council (EPSRC), grant reference number EP/T017899/1.
Glasgow Author(s) Enlighten ID:Morales, Professor Juan and Gaskell, Dr Jennifer and Husmeier, Professor Dirk and Torney, Professor Colin and Campioni, Nazareno
Authors: Campioni, N., Husmeier, D., Morales, J., Gaskell, J., and Torney, C. J.
College/School:College of Science and Engineering
College of Science and Engineering > School of Mathematics and Statistics > Mathematics
College of Science and Engineering > School of Mathematics and Statistics > Statistics
College of Medical Veterinary and Life Sciences > School of Biodiversity, One Health & Veterinary Medicine
Journal Name:Physical Review Research
Publisher:American Physical Society
ISSN (Online):2643-1564
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Algebras and Representation Theory Physical Review Research 3(4):043074
Publisher Policy:Reproduced under a Creative Commons licence

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
303337Multiscale methods for inferring the structure and dynamics of collective animal behaviourColin TorneyLeverhulme Trust (LEVERHUL)RPG-2018-398M&S - Mathematics
308255The SofTMech Statistical Emulation and Translation HubDirk HusmeierEngineering and Physical Sciences Research Council (EPSRC)EP/T017899/1M&S - Statistics