Dimension reduction of noisy interacting systems

Zagli, N., Pavliotis, G. A., Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471 and Alecio, A. (2023) Dimension reduction of noisy interacting systems. Physical Review Research, 5 (1). 013078. ISSN 2643-1564 doi: 10.1103/PhysRevResearch.5.013078

Abstract/Summary

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally, nonequilibrium setting. We provide a systematic dimension reduction methodology for constructing low-dimensional, reduced-order dynamics based on the cumulants of the probability distribution of the infinite system. We show that the low-dimensional dynamics returns the correct diagnostic properties since it produces a quantitatively accurate representation of the stationary phase diagram of the system that we compare with exact analytical results and numerical simulations. Moreover, we prove that the reduced order dynamics yields also the prognostic, i.e., time-dependent properties, as it provides the correct response of the system to external perturbations. On the one hand, this validates the use of our complexity reduction methodology since it retains information not only of the invariant measure of the system but also of the transition probabilities and time-dependent correlation properties of the stochastic dynamics. On the other hand, the breakdown of linear response properties is a key signature of the occurence of a phase transition. We show that the reduced response operators capture the correct diverging resonant behavior by quantitatively assessing the singular nature of the susceptibility of the system and the appearance of a pole for real values of frequencies. Hence, this methodology can be interpreted as a low-dimensional, reduced order approach to the investigation and detection of critical phenomena in high-dimensional interacting systems in settings where order parameters are not known.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/109629
Identification Number/DOI	10.1103/PhysRevResearch.5.013078
Refereed	Yes
Divisions	Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE) Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	APS
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